# LPTMS Publications

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## A Trap Model for Clogging and Unclogging in Granular Hopper Flows

### Alexandre Nicolas

^{1}Angel Garcimartín^{2}Iker Zuriguel^{2}*Physical Review Letters*, American Physical Society, 2018, 120 (19), pp.198002. 〈https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.198002〉- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. UNAV - Universidad de Navarra [Pamplona]

## Archive ouverte HAL – A correlation-hole approach to the electric double layer with counter-ions only

### Ivan Palaia

^{1}Martin Trulsson^{2}L. Samaj^{3}Emmanuel Trizac^{1}Ladislav Šamaj^{3}*Molecular Physics*, Taylor & Francis, 2018, 116 (21-22), pp.3134 - 3146. 〈10.1080/00268976.2018.1471234〉We study a classical system of identically charged counter-ions near a planar wall carrying a uniform surface charge density. The equilibrium statistical mechanics of the system depends on a single dimensionless coupling parameter. A new self-consistent theory of the correlation-hole type is proposed which leads to a modified Poisson-Boltzmann integral equation for the density profile, convenient for analytical progress and straightforward to solve numerically. The exact density profiles are recovered in the limits of weak and strong couplings. In contrast to previous theoretical attempts of the test-charge family, the density profiles fulfill the contact-value theorem at all values of the coupling constant, and exhibit the mean-field decay at asymptotically large distances from the wall, as expected. We furthermore show that the density corrections at large couplings exhibit the proper dependence on coupling parameter and distance to the charged wall. The numerical results for intermediate values of the coupling provide accurate density profiles which are in good agreement with those obtained by Monte-Carlo simulations. The crossover to mean-field behavior at large distance is studied in detail.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Lund University [Lund]
- 3. Institute of Physics

## Archive ouverte HAL – A counterintuitive way to speed up pedestrian and granular bottleneck flows prone to clogging: Can ‘more’ escape faster?

### Alexandre Nicolas

^{1}Santiago Ibáñez^{2}Marcelo Kuperman^{2}Sebastián Bouzat^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2018, 2018 (8), pp.083403. 〈http://iopscience.iop.org/article/10.1088/1742-5468/aad6c0〉Dense granular flows through constrictions, as well as competitive pedestrian evacuations, are hindered by a propensity to form clogs. We use simulations of model pedestrians and experiments with granular disks to explore an original strategy to speed up these flows, which consists in including contact-averse entities in the assembly. On the basis of a minimal cellular automaton and a continuous agent-based model for pedestrian evacuation dynamics, we find that the inclusion of polite pedestrians amid a given competitive crowd fails to reduce the evacuation time when the constriction (the doorway) is acceptably large. This is not surprising, because adding agents makes the crowd larger. In contrast, when the door is so narrow that it can accommodate at most one or two agents at a time, our strategy succeeds in substantially curbing long-lived clogs and speeding up the evacuation. A similar effect is seen experimentally in a vibrated two-dimensional hopper flow with an opening narrower than 3 disk diameters. Indeed, by adding to the initial collection of neutral disks a large fraction of magnetic ones, interacting repulsively, we observe a shortening of the time intervals between successive egresses of neutral disks, as reflected by the study of their probability distribution. On a more qualitative note, our study suggests that the much discussed analogy between pedestrian flows and granular flows could be extended to some behavioural traits of individual pedestrians.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Centro Atómico Bariloche [Argentine]

## Archive ouverte HAL – A Minimal Power Model for Human Running Performance

### Matthew Mulligan

^{1}Guillaume Adam^{2}Thorsten Emig^{3, 4}*PLoS ONE*, Public Library of Science, 2018Models for human running performances of various complexities and underlying principles have been proposed, often combining data from world record performances and bio-energetic facts of human physiology. Here we present a novel, minimal and universal model for human running performance that employs a relative metabolic power scale. The main component is a self-consistency relation for the time dependent maximal power output. The analytic approach presented here is the first to derive the observed logarithmic scaling between world (and other) record running speeds and times from basic principles of metabolic power supply. Various female and male record performances (world, national) and also personal best performances of individual runners for distances from 800m to the marathon are excellently described by this model, with mean errors of (often much) less than 1%. The model defines endurance in a way that demonstrates symmetry between long and short racing events that are separated by a characteristic time scale comparable to the time over which a runner can sustain maximal oxygen uptake. As an application of our model, we derive personalized characteristic race speeds for different durations and distances.

- 1. Claremont Mckenna College - CMC (USA)
- 2. (MSC)2 UMI3466 CNRS-MIT - Multi-Scale Material Science for Energy and Environment
- 3. MIT - Massachusetts Institute of Technology
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – A nonequilibrium force can stabilize 2D active nematics

### Ananyo Maitra

^{1, *}Pragya Srivastava^{2}M. Cristina Marchetti^{3}Juho Lintuvuori^{4}Sriram Ramaswamy^{5, 6}Martin Lenz^{1, 7, *}*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2018, 115 (27), pp.6934-6939Suspensions of actively driven anisotropic objects exhibit distinctively nonequilibrium behaviors, and current theories predict that they are incapable of sustaining orientational order at high activity. By contrast, here we show that nematic suspensions on a substrate can display order at arbitrarily high activity due to a previously unreported, potentially stabilizing active force. This force moreover emerges inevitably in theories of active orientable fluids under geometric confinement. The resulting nonequilibrium ordered phase displays robust giant number fluctuations that cannot be suppressed even by an incompressible solvent. Our results apply to virtually all experimental assays used to investigate the active nematic ordering of self-propelled colloids, bacterial sus-pensions, and the cytoskeleton and have testable implications in interpreting their nonequilibrium behaviors.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Theoretical Physics of Biology Laboratory
- 3. Department of Physics [Syracuse]
- 4. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 5. TIFR - Tata Institute of Fundamental Research [Hyderabad]
- 6. Centre for Condensed Matter Theory [Bangalore]
- 7. MSE2 - Multiscale Materials Science for Energy and Environment

## Archive ouverte HAL – A Trap Model for Clogging and Unclogging in Granular Hopper Flows

### Alexandre Nicolas

^{1}Angel Garcimartín^{2}Iker Zuriguel^{2}*Physical Review Letters*, American Physical Society, 2018, 120 (19), pp.198002. 〈https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.198002〉- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. UNAV - Universidad de Navarra [Pamplona]

## Archive ouverte HAL – Active Brownian motion in two dimensions

### Urna Basu

^{1}Satya N. Majumdar^{2}Alberto Rosso^{2}Satya Majumdar^{2}Gregory Schehr^{2}*Physical Review E*, American Physical Society (APS), 2018, 98 (6), 〈10.1103/PhysRevE.98.062121〉We study the dynamics of a single active Brownian particle (ABP) in a two-dimensional harmonic trap. The active particle has an intrinsic time scale $D_R^{-1}$ set by the rotational diffusion with diffusion constant $D_R$. The harmonic trap also induces a relaxational time-scale $\mu^{-1}$. We show that the competition between these two time scales leads to a nontrivial time evolution for the ABP. At short times a strongly anisotropic motion emerges leading to anomalous persistence/first-passage properties. At long-times, the stationary position distribution in the trap exhibits two different behaviours: a Gaussian peak at the origin in the strongly passive limit ($D_R \to \infty$) and a delocalised ring away from the origin in the opposite strongly active limit ($D_R \to 0$). The predicted stationary behaviours in these limits are in agreement with recent experimental observations.

- 1. Theoretical Condensed Matter Physics Division
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Asymptotics for the expected maximum of random walks and Lévy flights with a constant drift

### Philippe Mounaix

^{1}Satya N. Majumdar^{2}Satya Majumdar^{2}Gregory Schehr^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2018, 2018 (8), 〈10.1088/1742-5468/aad364〉In this paper, we study the large $n$ asymptotics of the expected maximum of an $n$-step random walk/L\'evy flight (characterized by a L\'evy index $1<\mu\leq 2$) on a line, in the presence of a constant drift $c$. For $0<\mu\leq 1$, the expected maximum is infinite, even for finite values of $n$. For $1<\mu\leq 2$, we obtain all the non-vanishing terms in the asymptotic expansion of the expected maximum for large $n$. For $c<0$ and $\mu =2$, the expected maximum approaches a non-trivial constant as $n$ gets large, while for $1<\mu < 2$, it grows as a power law $\sim n^{2-\mu}$. For $c>0$, the asymptotic expansion of the expected maximum is simply related to the one for $c<0$ by adding to the latter the linear drift term $cn$, making the leading term grow linearly for large $n$, as expected. Finally, we derive a scaling form interpolating smoothly between the cases $c=0$ and $c\ne 0$. These results are borne out by numerical simulations in excellent agreement with our analytical predictions.

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Band connectivity for topological quantum chemistry: Band structures as a graph theory problem

### Barry Bradlyn

^{1}L. Elcoro^{2}M. G. Vergniory^{2}Jennifer Cano^{1}Zhijun Wang^{1}C. Felser^{3}M. I. Aroyo^{2}B. Andrei Bernevig^{4, 5, 6}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 97 (3), 〈10.1103/PhysRevB.97.035138〉The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a recent paper [B. Bradlyn et al., Nature 547, 298 (2017)], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local "k-dot-p" band structures across the Brillouin zone in terms of graph theory. In the current manuscript we give the details of our full theoretical construction. We show that crystal symmetries strongly constrain the allowed connectivities of energy bands, and we employ graph-theoretic techniques such as graph connectivity to enumerate all the solutions to these constraints. The tools of graph theory allow us to identify disconnected groups of bands in these solutions, and so identify topologically distinct insulating phases.

- 1. Princeton University, Princeton, NJ 08544, USA
- 2. University of the Basque Country - University of the Basque Country
- 3. CPfS - Max Planck Institute for Chemical Physics of Solids
- 4. DPPU - Department of Physics,Princeton University
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. LPA - Laboratoire Pierre Aigrain

## Archive ouverte HAL – Building blocks of topological quantum chemistry: Elementary band representations

### Jennifer Cano

^{1}Barry Bradlyn^{1}Zhijun Wang^{1}L. Elcoro^{2}M. G. Vergniory^{2}C. Felser^{3}M. I. Aroyo^{2}B. Andrei Bernevig^{4, 5, 6}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 97 (3), 〈10.1103/PhysRevB.97.035139〉The link between chemical orbitals described by local degrees of freedom and band theory, which is defined in momentum space, was proposed by Zak several decades ago for spinless systems with and without time-reversal in his theory of "elementary" band representations. In Nature 547, 298-305 (2017), we introduced the generalization of this theory to the experimentally relevant situation of spin-orbit coupled systems with time-reversal symmetry and proved that all bands that do not transform as band representations are topological. Here, we give the full details of this construction. We prove that elementary band representations are either connected as bands in the Brillouin zone and are described by localized Wannier orbitals respecting the symmetries of the lattice (including time-reversal when applicable), or, if disconnected, describe topological insulators. We then show how to generate a band representation from a particular Wyckoff position and determine which Wyckoff positions generate elementary band representations for all space groups. This theory applies to spinful and spinless systems, in all dimensions, with and without time reversal. We introduce a homotopic notion of equivalence and show that it results in a finer classification of topological phases than approaches based only on the symmetry of wavefunctions at special points in the Brillouin zone. Utilizing a mapping of the band connectivity into a graph theory problem, which we introduced in Nature 547, 298-305 (2017), we show in companion papers which Wyckoff positions can generate disconnected elementary band representations, furnishing a natural avenue for a systematic materials search.

- 1. Princeton University, Princeton, NJ 08544, USA
- 2. University of the Basque Country - University of the Basque Country
- 3. CPfS - Max Planck Institute for Chemical Physics of Solids
- 4. DPPU - Department of Physics,Princeton University
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. LPA - Laboratoire Pierre Aigrain

## Archive ouverte HAL – Cell contraction induces long-ranged stress stiffening in the extracellular matrix

### Yu Long Han

^{1}Pierre Ronceray^{2}Guoqiang Xu^{1}Andrea Malandrino^{3, 1}Roger Kamm^{1}Martin Lenz^{4}Chase P. Broedersz^{5}Ming Guo^{1}*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2018Animal cells in tissues are supported by biopolymer matrices, which typically exhibit highly nonlinear mechanical properties. While the linear elasticity of the matrix can significantly impact cell mechanics and functionality, it remains largely unknown how cells, in turn, affect the nonlinear mechanics of their surrounding matrix. Here we show that living contractile cells are able to generate a massive stiffness gradient in three distinct 3D extracellular matrix model systems: collagen, fibrin, and Matrigel. We decipher this remarkable behavior by introducing Nonlinear Stress Inference Microscopy (NSIM), a novel technique to infer stress fields in a 3D matrix from nonlinear microrheology measurement with optical tweezers. Using NSIM and simulations, we reveal a long-ranged propagation of cell-generated stresses resulting from local filament buckling. This slow decay of stress gives rise to the large spatial extent of the observed cell-induced matrix stiffness gradient, which could form a mechanism for mechanical communication between cells.

- 1. MIT - Massachusetts Institute of Technology
- 2. Princeton Center for Theoretical Science
- 3. IBEC - Institute for Bioengineering of Catalonia [Barcelona]
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Ludwig-Maximilians-Universität München

## Archive ouverte HAL – Collective Spin Modes of a Trapped Quantum Ferrofluid

### S. Lepoutre

^{1}L. GabardosK. KechadiP. Pedri^{2}O. Gorceix^{1}E. Maréchal^{3}L. Vernac^{1}B. Laburthe-Tolra^{1}*Physical Review Letters*, American Physical Society, 2018, 121 (1)- 1. LPL - Laboratoire de Physique des Lasers
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. inconnu

## Archive ouverte HAL – Correlations of occupation numbers in the canonical ensemble and application to a Bose-Einstein condensate in a one-dimensional harmonic trap

### Olivier Giraud

^{1}Aurélien Grabsch^{1}Christophe Texier^{1}*Physical Review A*, American Physical Society, 2018, 97 (5), 〈10.1103/PhysRevA.97.053615〉We study statistical properties of $N$ non-interacting identical bosons or fermions in the canonical ensemble. We derive several general representations for the $p$-point correlation function of occupation numbers $\overline{n_1\cdots n_p}$. We demonstrate that it can be expressed as a ratio of two $p\times p$ determinants involving the (canonical) mean occupations $\overline{n_1}$, ..., $\overline{n_p}$, which can themselves be conveniently expressed in terms of the $k$-body partition functions (with $k\leq N$). We draw some connection with the theory of symmetric functions, and obtain an expression of the correlation function in terms of Schur functions. Our findings are illustrated by revisiting the problem of Bose-Einstein condensation in a 1D harmonic trap, for which we get analytical results. We get the moments of the occupation numbers and the correlation between ground state and excited state occupancies. In the temperature regime dominated by quantum correlations, the distribution of the ground state occupancy is shown to be a truncated Gumbel law. The Gumbel law, describing extreme value statistics, is obtained when the temperature is much smaller than the Bose-Einstein temperature.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Dimensional crossover for the beyond-mean-field correction in Bose gases

### Tobias Ilg

^{1}Jan Kumlin^{1}Luis Santos^{2}Dmitry S. Petrov^{3}Hans Peter Büchler^{1}*Physical Review A*, American Physical Society, 2018, 98 (5), 〈10.1103/PhysRevA.98.051604〉We present a detailed beyond-mean-field analysis of a weakly interacting Bose gas in the crossover from three to low dimensions. We find an analytical solution for the energy and provide a clear qualitative picture of the crossover in the case of a box potential with periodic boundary conditions. We show that the leading contribution of the confinement-induced resonance is of beyond-mean-field order and calculate the leading corrections in the three- and low-dimensional limits. We also characterize the crossover for harmonic potentials in a model system with particularly chosen short- and long-range interactions and show the limitations of the local-density approximation. Our analysis is applicable to Bose-Bose mixtures and gives a starting point for developing the beyond-mean-field theory in inhomogeneous systems with long-range interactions such as dipolar particles or Rydberg-dressed atoms.

- 1. University of Stuttgart
- 2. LUH - Leibniz Universität Hannover [Hannover]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Dimer-dimer zero crossing and dilute dimerized liquid in a one-dimensional mixture

### A. Pricoupenko

^{1, 2}D. S. Petrov^{1}*Physical Review A*, American Physical Society, 2018, 97 (6), 〈10.1103/PhysRevA.97.063616〉We consider the system of dimers formed in a one-dimensional mass-balanced Bose-Bose mixture of species $\sigma=\uparrow$, $\downarrow$ with attractive interspecies and repulsive intraspecies contact interactions. In the plane parametrized by the ratios of the coupling constants $g_{\uparrow\uparrow}/|g_{\uparrow\downarrow}|$ and $g_{\downarrow\downarrow}/|g_{\uparrow\downarrow}|$ we trace out the curve where the dimer-dimer interaction switches from attractive to repulsive. We find this curve to be significantly (by more than a factor of 2) shifted towards larger $g_{\sigma\sigma}$ (or smaller $|g_{\uparrow\downarrow}|$) compared to the mean-field stability boundary $g_{\uparrow\uparrow}g_{\downarrow\downarrow}=g_{\uparrow\downarrow}^2$. For a weak dimer-dimer attraction we predict a dilute dimerized liquid phase stabilized against collapse by a repulsive three-dimer force.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. ENS Lyon - École normale supérieure - Lyon

## Archive ouverte HAL – Drag force and superfluidity in the supersolid stripe phase of a spin-orbit-coupled Bose-Einstein condensate

### Giovanni I. Martone

^{1}Georgy V. Shlyapnikov^{2, 1, 3, 4, 5}*Journal of Experimental and Theoretical Physics (JETP) / Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki*, MAIK Nauka/Interperiodica, 2018The phase diagram of a spin-orbit-coupled two-component Bose gas includes a supersolid stripe phase, which is featuring density modulations along the direction of the spin-orbit coupling. This phase has been recently found experimentally [J.~Li \textit{et al.}, Nature (London) \textbf{543}, 91 (2017)]. In the present work we characterize the superfluid behavior of the stripe phase by calculating the drag force acting on a moving impurity. Because of the gapless band structure of the excitation spectrum, the Landau critical velocity vanishes if the motion is not strictly parallel to the stripes, and energy dissipation takes place at any speed. Moreover, due to the spin-orbit coupling, the drag force can develop a component perpendicular to the velocity of the impurity. Finally, by estimating the time over which the energy dissipation occurs, we find that for slow impurities the effects of friction are negligible on a time scale up to several seconds, which is comparable with the duration of a typical experiment.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 3. Russian Quantum Center
- 4. SPEC - UMR3680 - Service de physique de l'état condensé
- 5. Wuhan Institute of Physics and Mathematics

## Archive ouverte HAL – Duality in Power-Law Localization in Disordered One-Dimensional Systems

### X. Deng

^{1}V. e. Kravtsov^{2, 3}G. v. Shlyapnikov^{4, 5, 6, 7, 8}L. Santos^{1}*Physical Review Letters*, American Physical Society, 2018, 120 (11), 〈10.1103/PhysRevLett.120.110602〉The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, $1/r^a$. For randomly spaced particles, these models present an effective peculiar disorder that leads to surprising localization properties. We show that in one-dimensional systems almost all eigenstates (except for a few states close to the ground state) are power-law localized for any value of $a>0$. Moreover, we show that our model is an example of a new universality class of models with power-law hopping, characterized by a duality between systems with long-range hops ($a<1$) and short-range hops ($a>1$) in which the wave function amplitude falls off algebraically with the same power $\gamma$ from the localization center.

- 1. LUH - Leibniz Universität Hannover [Hannover]
- 2. ICTP - Abdus Salam International Centre for Theoretical Physics [Trieste]
- 3. L.D. Landau Institute for Theoretical Physics of RAS
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. SPEC - UMR3680 - Service de physique de l'état condensé
- 6. Russian Quantum Center
- 7. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 8. Wuhan Institute of Physics and Mathematics

## Archive ouverte HAL – Effects of refractory period on stochastic resetting

### Martin R. Evans

^{1}Satya N. Majumdar^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2018We consider a stochastic process undergoing resetting after which a random refractory period is imposed. In this period the process is quiescent and remains at the resetting position. Using a first-renewal approach, we compute exactly the stationary position distribution and analyse the emergence of a delta peak at the resetting position. In the case of a power-law distribution for the refractory period we find slow relaxation. We generalise our results to the case when the resetting period and the refractory period are correlated, by computing the Laplace transform of the survival probability of the process and the mean first passage time, i.e., the mean time to completion of a task. We also compute exactly the joint distribution of the active and absorption time to a fixed target.

- 1. SUPA, School of Physics, University of Edinburgh
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Eigenfunction distribution for the Rosenzweig-Porter model

### E. Bogomolny

^{1}M. Sieber^{2}*Physical Review E*, American Physical Society (APS), 2018, 98 (3), 〈10.1103/PhysRevE.98.032139〉The statistical distribution of eigenfunctions for the Rosenzweig-Porter model is derived for the region where eigenfunctions have fractal behaviour. The result is based on simple physical ideas and leads to transparent explicit formulas which agree very well with numerical calculations. It constitutes a rare case where a non-trivial eigenfunction distribution is obtained in a closed form.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. School of Mathematics [Bristol]

## Archive ouverte HAL – Eigenstate versus Zeeman-based approaches to the solid effect

### Inés Rodríguez-Arias

^{1}Alberto Rosso^{1}Andrea De Luca^{2}*Magnetic Resonance in Chemistry*, Wiley, 2018, 56 (7), pp.689 - 698. 〈10.1002/mrc.4724〉The solid effect is one of the simplest and most effective mechanisms for Dynamic Nuclear Polarization. It involves the exchange of polarization between one electron and one nuclear spin coupled via the hyperfine interaction. Even for such a small spin system, the theoretical understanding is complicated by the contact with the lattice and the microwave irradiation. Both being weak, they can be treated within perturbation theory. In this work, we analyze the two most popular perturbation schemes: the Zeeman and the eigenstate-based approaches which differ in the way the hyperfine interaction is treated. For both schemes, we derive from first principles an effective Liouville equation which describes the density matrix of the spin system; we then study numerically the behavior of the nuclear polarization for several values of the hyperfine coupling. In general, we obtain that the Zeeman-based approach underestimates the value of the nuclear polarization. By performing a projection onto the diagonal part of the spin-system density matrix, we are able to understand the origin of the discrepancy, which is due to the presence of parasite leakage transitions appearing whenever the Zeeman basis is employed.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Rudolf Peierls Centre for Theoretical Physics

## Archive ouverte HAL – Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model

### Kirill Plekhanov

^{1, 2}Ivana Vasić^{3}Alexandru Petrescu^{4}Rajbir Nirwan^{5}Guillaume Roux^{2}Walter Hofstetter^{5}Karyn Le Hur^{1}*Physical Review Letters*, American Physical Society, 2018, 120 (15), 〈10.1103/PhysRevLett.120.157201〉Recently, the frustrated XY model for spins-1/2 on the honeycomb lattice has attracted a lot of attention in relation with the possibility to realize a chiral spin liquid state. This model is relevant to the physics of some quantum magnets. Using the flexibility of ultra-cold atoms setups, we propose an alternative way to realize this model through the Mott regime of the bosonic Kane-Mele-Hubbard model. The phase diagram of this model is derived using the bosonic dynamical mean-field theory. Focussing on the Mott phase, we investigate its magnetic properties as a function of frustration. We do find an emergent chiral spin state in the intermediate frustration regime. Using exact diagonalization we study more closely the physics of the effective frustrated XY model and the properties of the chiral spin state. This gapped phase displays a chiral order, breaking time-reversal and parity symmetry, but is not topologically ordered (the Chern number is zero).

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Institute of Physics [Belgrade]
- 4. EE - Department of Electrical Engineering [Princeton]
- 5. ITP - Institut für Theoretische Physik [Frankfurt am Main]

## Archive ouverte HAL – Energy of N two-dimensional bosons with zero-range interactions

### Betzalel Bazak

^{1}Dmitry S. Petrov^{2}*New Journal of Physics*, Institute of Physics: Open Access Journals, 2018, 20 (2), 〈10.1088/1367-2630/aaa64f〉We derive an integral equation describing $N$ two-dimensional bosons with zero-range interactions and solve it for the ground state energy $B_N$ by applying a stochastic diffusion Monte Carlo scheme for up to 26 particles. We confirm and go beyond the scaling $B_N\propto 8.567^N$ predicted by Hammer and Son [Phys. Rev. Lett. {\bf 93}, 250408 (2004)] in the large-$N$ limit.

- 1. IPNO - Institut de Physique Nucléaire d'Orsay
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Engineered Swift Equilibration for Brownian objects: from underdamped to overdamped dynamics

### Marie Chupeau

^{1}Sergio Ciliberto^{2}David Guéry-Odelin^{3}Emmanuel Trizac^{1}*New Journal of Physics*, Institute of Physics: Open Access Journals, 2018, 20 (7), pp.075003. 〈10.1088/1367-2630/aac875〉We propose a general framework to study transformations that drive an underdamped Brownian particle in contact with a thermal bath from an equilibrium state to a new one in an arbitrarily short time. To this end, we make use of a time and space-dependent potential, that plays a dual role: confine the particle, and manipulate the system. In the special case of an isothermal compression or decompression of a harmonically trapped particle, we derive explicit protocols that perform this quick transformation, following an inverse engineering method. We focus on the properties of these protocols, which crucially depend on two key dimensionless numbers that characterize the relative values of the three timescales of the problem, associated with friction, oscillations in the confinement and duration of the protocol. In particular, we show that our protocols encompass the known overdamped version of this problem and extend it to any friction for decompression and to a large range of frictions for compression.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 3. Atomes Froids (LCAR)

## Archive ouverte HAL – Entanglement evolution and generalised hydrodynamics: noninteracting systems

### Bruno BertiniMaurizio Fagotti

^{1}Lorenzo PiroliPasquale Calabrese*J.Phys.A*, 2018, 51 (39), pp.39LT01. 〈10.1088/1751-8121/aad82e〉The large-scale properties of homogeneous states after quantum quenches in integrable systems have been successfully described by a semiclassical picture of moving quasiparticles. Here we consider the generalisation for the entanglement evolution after an inhomogeneous quench in noninteracting systems in the framework of generalised hydrodynamics. We focus on the protocol where two semi-infinite halves are initially prepared in different states and then joined together, showing that a proper generalisation of the quasiparticle picture leads to exact quantitative predictions. If the system is initially prepared in a quasistationary state, we find that the entanglement entropy is additive and it can be computed by means of generalised hydrodynamics. Conversely, additivity is lost when the initial state is not quasistationary; yet the entanglement entropy in the large-scale limit can be exactly predicted in the quasiparticle picture, provided that the initial state is low entangled.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Exact Persistence Exponent for the 2 D -Diffusion Equation and Related Kac Polynomials

### Mihail Poplavskyi

^{1}Gregory Schehr^{2}*Physical Review Letters*, American Physical Society, 2018, 121 (15), 〈10.1103/PhysRevLett.121.150601〉We compute the persistence for the $2d$-diffusion equation with random initial condition, i.e., the probability $p_0(t)$ that the diffusion field, at a given point ${\bf x}$ in the plane, has not changed sign up to time $t$. For large $t$, we show that $p_0(t) \sim t^{-\theta(2)}$ with $\theta(2) = 3/16$. Using the connection between the $2d$-diffusion equation and Kac random polynomials, we show that the probability $q_0(n)$ that Kac polynomials, of (even) degree $n$, have no real root decays, for large $n$, as $q_0(n) \sim n^{-3/4}$. We obtain this result by using yet another connection with the truncated orthogonal ensemble of random matrices. This allows us to compute various properties of the zero-crossings of the diffusing field, equivalently of the real roots of Kac polynomials. Finally, we unveil a precise connection with a fourth model: the semi-infinite Ising spin chain with Glauber dynamics at zero temperature.

- 1. King's College
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Exactly solvable model for dynamic nuclear polarization

### Inés Rodríguez-Arias

^{1}Markus Müller^{2, 3}Alberto Rosso^{1}Andrea De Luca^{4}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 98 (22), 〈10.1103/PhysRevB.98.224202〉We introduce a solvable model of driven fermions that elucidates the role of the localization transition in driven disordered magnets, as used in the context of dynamic nuclear polarization. Instead of spins, we study a set of non-interacting fermions that are coupled locally to nuclear spins and tend to hyperpolarize them. The induced hyperpolarization is a fingerprint of the driven steady state of the fermions, which undergo an Anderson Localization (AL) transition upon increasing the disorder. Our central result is that the maximal hyperpolarization level is always found close to the localization transition. In the limit of small nuclear moments the maximum is pinned to the transition, and the hyperpolarization is strongly enhanced by multi-fractal correlations in the critical state of the nearly localized driven system, its magnitude reflecting multi-fractal scaling.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. PSI - Paul Scherrer Institute
- 3. ICTP - Abdus Salam International Centre for Theoretical Physics [Trieste]
- 4. Rudolf Peierls Center for Theoretical Physics

## Archive ouverte HAL – Exponential number of equilibria and depinning threshold for a directed polymer in a random potential

### Yan V Fyodorov

^{1}Pierre Le Doussal^{2}Alberto Rosso^{3}Christophe Texier^{3}Yan Fyodorov^{4}Pierre Le Doussal^{2}*Annals of Physics*, 2018, 397, pp.1 - 64. 〈10.1016/j.aop.2018.07.029〉By extending the Kac-Rice approach to manifolds of finite internal dimension, we show that the mean number $\left\langle\mathcal{N}_\mathrm{tot}\right\rangle$ of all possible equilibria (i.e. force-free configurations, a.k.a. equilibrium points) of an elastic line (directed polymer), confined in a harmonic well and submitted to a quenched random Gaussian potential in dimension $d=1+1$, grows exponentially $\left\langle\mathcal{N}_\mathrm{tot}\right\rangle\sim\exp{(r\,L)}$ with its length $L$. The growth rate $r$ is found to be directly related to the generalised Lyapunov exponent (GLE) which is a moment-generating function characterising the large-deviation type fluctuations of the solution to the initial value problem associated with the random Schr\"odinger operator of the 1D Anderson localization problem. For strong confinement, the rate $r$ is small and given by a non-perturbative (instanton, Lifshitz tail-like) contribution to GLE. For weak confinement, the rate $r$ is found to be proportional to the inverse Larkin length of the pinning theory. As an application, identifying the depinning with a landscape "topology trivialization" phenomenon, we obtain an upper bound for the depinning threshold $f_c$, in the presence of an applied force, for elastic lines and $d$-dimensional manifolds, expressed through the mean modulus of the spectral determinant of the Laplace operators with a random potential. We also discuss the question of counting of stable equilibria. Finally, we extend the method to calculate the asymptotic number of equilibria at fixed energy (elastic, potential and total), and obtain the (annealed) distribution of the energy density over these equilibria (i.e. force-free configurations). Some connections with the Larkin model are also established.

- 1. School of Mathematical Sciences [ Nottingham]
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. School of Mathematical Sciences [London]

## Archive ouverte HAL – Extrapolation to Nonequilibrium from Coarse-Grained Response Theory

### Urna Basu

^{1, 2}Laurent Helden^{3}Matthias Krüger^{4, 3, 5}*Physical Review Letters*, American Physical Society, 2018, 120 (18), 〈10.1103/PhysRevLett.120.180604〉Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far from equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many body systems. It is illustrated in a four state model and in the near critical Ising model.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
- 3. University of Stuttgart
- 4. Max Planck Institute for Intelligent Systems
- 5. Georg-August-University [Göttingen]

## Archive ouverte HAL – Extreme statistics and index distribution in the classical 1 d Coulomb gas

### Abhishek Dhar

^{1}Anupam Kundu^{1}Satya N. Majumdar^{2}Sanjib Sabhapandit^{3}Gregory Schehr^{2}Satya Majumdar^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2018, 51 (29), 〈10.1088/1751-8121/aac75f〉We consider a one-dimensional gas of $N$ charged particles confined by an external harmonic potential and interacting via the one-dimensional Coulomb potential. For this system we show that in equilibrium the charges settle, on an average, uniformly and symmetrically on a finite region centred around the origin. We study the statistics of the position of the rightmost particle $x_{\max}$ and show that the limiting distribution describing its typical fluctuations is different from the Tracy-Widom distribution found in the one-dimensional log-gas. We also compute the large deviation functions which characterise the atypical fluctuations of $x_{\max}$ far away from its mean value. In addition, we study the gap between the two rightmost particles as well as the index $N_+$, i.e., the number of particles on the positive semi-axis. We compute the limiting distributions associated to the typical fluctuations of these observables as well as the corresponding large deviation functions. We provide numerical supports to our analytical predictions. Part of these results were announced in a recent Letter, Phys. Rev. Lett. 119, 060601 (2017).

- 1. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Raman Research Institute

## Archive ouverte HAL – Finite-Temperature Disordered Bosons in Two Dimensions

### G. Bertoli

^{1}V. p. Michal^{2}B. l. Altshuler^{3}G. v. Shlyapnikov^{1}*Physical Review Letters*, American Physical Society, 2018, 121 (3), 〈10.1103/PhysRevLett.121.030403〉We study phase transitions in a two dimensional weakly interacting Bose gas in a random potential at finite temperatures. We identify superfluid, normal fluid, and insulator phases and construct the phase diagram. At T=0 one has a tricritical point where the three phases coexist. The truncation of the energy distribution at the trap barrier, which is a generic phenomenon in cold atom systems, limits the growth of the localization length and in contrast to the thermodynamic limit the insulator phase is present at any temperature.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. TU Delft - Delft University of Technology
- 3. Columbia University [New York]

## Archive ouverte HAL – Fluctuations of observables for free fermions in a harmonic trap at finite temperature

### Aurélien Grabsch

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}Christophe Texier^{1}*SciPost Physics Journals*, the SciPost Foundation, 2018We study a system of 1D noninteracting spinless fermions in a confining trap at finite temperature. We first derive a useful and general relation for the fluctuations of the occupation numbers valid for arbitrary confining trap, as well as for both canonical and grand canonical ensembles. Using this relation, we obtain compact expressions, in the case of the harmonic trap, for the variance of certain observables of the form of sums of a function of the fermions' positions, $\mathcal{L}=\sum_n h(x_n)$. Such observables are also called linear statistics of the positions. As anticipated, we demonstrate explicitly that these fluctuations do depend on the ensemble in the thermodynamic limit, as opposed to averaged quantities, which are ensemble independent. We have applied our general formalism to compute the fluctuations of the number of fermions $\mathcal{N}_+$ on the positive axis at finite temperature. Our analytical results are compared to numerical simulations. We discuss the universality of the results with respect to the nature of the confinement.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Full Dysonian dynamics of the complex Ginibre ensemble

### Jacek Grela

^{1}Piotr Warchoł*J.Phys.A*, 2018, 51 (42), pp.425203. 〈10.1088/1751-8121/aadd54〉We find stochastic equations governing eigenvalues and eigenvectors of a dynamical complex Ginibre ensemble reaffirming the intertwined role played between both sets of matrix degrees of freedom. We solve the accompanying Smoluchowski–Fokker–Planck equation valid for any initial matrix. We derive evolution equations for the averaged extended characteristic polynomial and for a class of k-point eigenvalue correlation functions. From the latter we obtain a novel formula for the eigenvector correlation function which we inspect for Ginibre and spiric initial conditions and obtain macro- and microscopic limiting laws.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Ground-state energy of noninteracting fermions with a random energy spectrum

### Hendrik SchaweAlexander K. HartmannSatya N. Majumdar

^{1}Grégory Schehr^{1}*EPL*, 2018, 124 (4), pp.40005. 〈10.1209/0295-5075/124/40005〉We derive analytically the full distribution of the ground-state energy of K non-interacting fermions in a disordered environment, modelled by a Hamiltonian whose spectrum consists of N i.i.d. random energy levels with distribution (with ε ≥ 0), in the same spirit as the “Random Energy Model”. We show that for each fixed K, the distribution P K, N (E 0) of the ground-state energy E 0 has a universal scaling form in the limit of large N. We compute this universal scaling function and show that it depends only on K and the exponent α characterizing the small ε behaviour of . We compared the analytical predictions with results from numerical simulations. For this purpose we employed a sophisticated importance-sampling algorithm that allowed us to obtain the distributions over a large range of the support down to probabilities as small as . We found asymptotically a very good agreement between analytical predictions and numerical results.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – High-precision simulation of the height distribution for the KPZ equation

### Alexander K. Hartmann

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}Alberto Rosso^{3}Gregory Schehr^{3}*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2018, 121 (6), 〈10.1209/0295-5075/121/67004〉The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling approach, the distribution is obtained over a large range of values, down to a probability density as small as 10^{-1000} in the tails. Both short and long times are investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations. At short times the agreement with the analytical expression is spectacular. We observe that the far left and right tails, with exponents 5/2 and 3/2 respectively, are preserved until large time. We present some evidence for the predicted non-trivial crossover in the left tail from the 5/2 tail exponent to the cubic tail of Tracy-Widom, although the details of the full scaling form remains beyond reach.

- 1. University of Oldenburg
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Higher-order corrections to the effective potential close to the jamming transition in the perceptron model

### Ada Altieri

^{1, 2}*Physical Review E*, American Physical Society (APS), 2018, 97 (1), 〈10.1103/PhysRevE.97.012103〉We analyze the perceptron model performing a Plefka-like expansion of the free energy. This model falls in the same universality class as hard spheres near jamming, allowing to get exact predictions in high dimensions for more complex systems. Our method enables to define an effective potential (or TAP free energy), namely a coarse-grained functional depending on the contact forces and the effective gaps between the particles. The derivation is performed up to the third order, with a particular emphasis on the role of third order corrections to the TAP free energy. These corrections, irrelevant in a mean-field framework in the thermodynamic limit, might instead play a fundamental role when considering finite-size effects. We also study the typical behavior of the forces and we show that two kinds of corrections can occur. The first contribution arises since the system is analyzed at a finite distance from jamming, while the second one is due to finite-size corrections. In our analysis, third order contributions vanish in the jamming limit, both for the potential and the generalized forces, in agreement with the argument proposed by Wyart and coworkers invoking isostaticity. Finally, we analyze the scalings emerging close to the jamming line, which define a crossover regime connecting the control parameters of the model to an effective temperature.

- 1. Department of Physics [Roma La Sapienza]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Hofstadter point spectrum trace and the Almost Mathieu operator

### Stephane Ouvry

^{1}Stephan Wagner^{2}Shuang Wu^{1}*Journal of Mathematical Physics*, American Institute of Physics (AIP), 2018We consider point spectrum traces in the Hofstadter model. We show how to recover the full quantum Hofstadter trace by integrating these point spectrum traces with the appropriate free density of states on the lattice. This construction is then generalized to the almost Mathieu operator and its n-th moments which can be expressed in terms of generalized Kreft coefficients.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Stellenbosch University

## Archive ouverte HAL – Large deviations of convex hulls of self-avoiding random walks

### Hendrik Schawe

^{1}Alexander K. Hartmann^{2}Satya N. Majumdar^{3}Alexander HartmannSatya Majumdar^{3}*Physical Review E*, American Physical Society (APS), 2018, 97 (6), 〈10.1103/PhysRevE.97.062159〉A global picture of a random particle movement is given by the convex hull of the visited points. We obtained numerically the probability distributions of the volume and surface of the convex hulls of a selection of three types of self-avoiding random walks, namely the classical Self-Avoiding Walk, the Smart-Kinetic Self-Avoiding Walk, and the Loop-Erased Random Walk. To obtain a comprehensive description of the measured random quantities, we applied sophisticated large-deviation techniques, which allowed us to obtain the distributions over a large range of the support down to probabilities far smaller than $P = 10^{-100}$ . We give an approximate closed form of the so-called large-deviation rate function $\Phi$ which generalizes above the upper critical dimension to the previously studied case of the standard random walk. Further we show correlations between the two observables also in the limits of atypical large or small values.

- 1. University of Oldenburg
- 2. Institut für Physik
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Like-charge attraction in a one-dimensional setting: the importance of being odd

### E. Trizac

^{1}G. Tellez^{2}*European Journal of Physics*, European Physical Society, 2018From cement cohesion to DNA condensation, a proper statistical physics treatment of systems with long range forces is important for a number of applications in physics, chemistry, and biology. We compute here the effective force between fixed charged macromolecules, screened by oppositely charged mobile ions (counterions). We treat the problem in a one dimensional configuration, that allows for interesting discussion and derivation of exact results, remaining at a level of mathematical difficulty compatible with an undergraduate course. Emphasis is put on the counter-intuitive but fundamental phenomenon of like-charge attraction, that our treatment brings for the first time to the level of undergraduate teaching. The parity of the number of counterions is shown to play a prominent role, which sheds light on the binding mechanism at work when like-charge macromolecules do attract.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Departamento de Fisica

## Archive ouverte HAL – Liquid beyond the van der Waals paradigm

### Dmitry Petrov

^{1}*Nature Physics*, Nature Publishing Group, 2018, 14 (3), pp.211 - 212. 〈10.1038/s41567-018-0052-9〉- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Localization of soft modes at the depinning transition

### Xiangyu Cao

^{1}Sebastián Bouzat^{2}Alejandro B. Kolton^{2}Alberto Rosso^{1}*Physical Review E*, American Physical Society (APS), 2018, 97 (2), 〈10.1103/PhysRevE.97.022118〉We characterize the soft modes of the dynamical matrix at the depinning transition, and compare it with the properties of the Anderson model (and long--range generalizations). The density of states at the edge of the spectrum displays a universal linear tail, different from the Lifshitz tails. The eigenvectors are instead very similar in the two matrix ensembles. We focus on the ground state (soft mode), which represents the epicenter of avalanche instabilities. We expect it to be localized in all finite dimensions, and make a clear connection between its localization length and the Larkin length of the depinning model. In the fully connected model, the weak--strong pinning transition coincides with a peculiar localization transition of the ground state.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Centro Atómico Bariloche [Argentine]

## Archive ouverte HAL – Log-correlated random-energy models with extensive free-energy fluctuations: Pathologies caused by rare events as signatures of phase transitions

### Xiangyu Cao

^{1}Yan FyodorovPierre Le Doussal^{2}*Phys.Rev.E*, 2018, 97 (2), pp.022117. 〈10.1103/PhysRevE.97.022117〉We address systematically an apparent nonphysical behavior of the free-energy moment generating function for several instances of the logarithmically correlated models: the fractional Brownian motion with Hurst index H=0 (fBm0) (and its bridge version), a one-dimensional model appearing in decaying Burgers turbulence with log-correlated initial conditions and, finally, the two-dimensional log-correlated random-energy model (logREM) introduced in Cao et al. [Phys. Rev. Lett. 118, 090601 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.090601] based on the two-dimensional Gaussian free field with background charges and directly related to the Liouville field theory. All these models share anomalously large fluctuations of the associated free energy, with a variance proportional to the log of the system size. We argue that a seemingly nonphysical vanishing of the moment generating function for some values of parameters is related to the termination point transition (i.e., prefreezing). We study the associated universal log corrections in the frozen phase, both for logREMs and for the standard REM, filling a gap in the literature. For the above mentioned integrable instances of logREMs, we predict the nontrivial free-energy cumulants describing non-Gaussian fluctuations on the top of the Gaussian with extensive variance. Some of the predictions are tested numerically.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Archive ouverte HAL – Mapping the Calogero model on the Anyon model

### Stéphane Ouvry

^{1}Alexios P. Polychronakos*Nucl.Phys.B*, 2018, 936, pp.189-205. 〈10.1016/j.nuclphysb.2018.09.011〉We explicitly map the N -body one dimensional Calogero eigenstates in a harmonic well to the lowest Landau level sector of N -body eigenstates of the two dimensional anyon model in a harmonic well. The mapping is achieved in terms of a convolution kernel that uses as input the scattering eigenstates of the free Calogero model on the infinite line, which are obtained in an operator formulation.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Matrix product algorithm for stochastic dynamics on networks applied to nonequilibrium Glauber dynamics

### Thomas Barthel

^{1, 2}Caterina De Bacco^{2, 3}Silvio Franz^{2}*Physical Review E*, American Physical Society (APS), 2018, 97 (1), 〈10.1103/PhysRevE.97.010104〉We introduce and apply a novel efficient method for the precise simulation of stochastic dynamical processes on locally tree-like graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for example, to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon ideas from quantum many-body theory, the new approach is based on a matrix product approximation of the so-called edge messages -- conditional probabilities of vertex variable trajectories. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the matrix product edge messages (MPEM) in truncations. In contrast to Monte Carlo simulations, the algorithm has a better error scaling and works for both, single instances as well as the thermodynamic limit. We employ it to examine prototypical non-equilibrium Glauber dynamics in the kinetic Ising model. Because of the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations.

- 1. Duke university [Durham]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Santa Fe Institute

## Archive ouverte HAL – Matrix product state description of Halperin states

### V. Crépel

^{1}B. Estienne^{2}B.A. Bernevig^{1, 3}P. Lecheminant^{4}N. Regnault^{1}*Phys.Rev.B*, 2018, 97 (16), pp.165136. 〈10.1103/PhysRevB.97.165136〉Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact matrix product state (MPS) that was extensively studied for the systems without any spin or any other internal degrees of freedom. In that case, the correlators are built from a single electronic operator, which is primary with respect to the underlying conformal field theory. We generalize this construction to the archetype of Abelian multicomponent fractional quantum Hall wave functions, the Halperin states. These can be written as conformal blocks involving multiple electronic operators and we explicitly derive their exact MPS representation. In particular, we deal with the caveat of the full wave-function symmetry and show that any additional SU(2) symmetry is preserved by the natural MPS truncation scheme provided by the conformal dimension. We use our method to characterize the topological order of the Halperin states by extracting the topological entanglement entropy. We also evaluate their bulk correlation lengths, which are compared to plasma analogy arguments.

- 1. LPA - Laboratoire Pierre Aigrain
- 2. LPTHE - Laboratoire de Physique Théorique et Hautes Energies
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. LPTM - Laboratoire de Physique Théorique et Modélisation

## Archive ouverte HAL – Modeling of networks and globules of charged domain walls observed in pump and pulse induced states

### Petr Karpov

^{1}Serguei Brazovskii^{2, 1, 3}*Scientific Reports*, Nature Publishing Group, 2018Experiments on optical and STM injection of carriers in layered $\mathrm{MX_2}$ materials revealed the formation of nanoscale patterns with networks and globules of domain walls. This is thought to be responsible for the metallization transition of the Mott insulator and for stabilization of a "hidden" state. In response, here we present studies of the classical charged lattice gas model emulating the superlattice of polarons ubiquitous to the material of choice $1T-\mathrm{TaS_2}$. The injection pulse was simulated by introducing a small random concentration of voids which subsequent evolution was followed by means of Monte Carlo cooling. Below the detected phase transition, the voids gradually coalesce into domain walls forming locally connected globules and then the global network leading to a mosaic fragmentation into domains with different degenerate ground states. The obtained patterns closely resemble the experimental STM visualizations. The surprising aggregation of charged voids is understood by fractionalization of their charges across the walls' lines.

- 1. MISIS - National University of Science and Technology
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. IJS - Jozef Stefan Institute [Ljubljana, Slovenia]

## Archive ouverte HAL – Modified Szegö–Widom Asymptotics for Block Toeplitz Matrices with Zero Modes

### E. BasorJerome Dubail

^{1}T. Emig^{2}R. Santachiara^{3}*Journal of Statistical Physics*, Springer Verlag, 2018- 1. LPCT - Laboratoire de Physique et Chimie Théoriques
- 2. MIT - Massachusetts Institute of Technology
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Momentum correlations as signature of sonic Hawking radiation in Bose-Einstein condensates

### A. Fabbri

^{1}N. Pavloff^{2}*SciPost Phys.*, 2018, 4, pp.019. 〈10.21468/SciPostPhys.4.4.019〉We study the two-body momentum correlation signal in a quasi one dimensional Bose-Einstein condensate in the presence of a sonic horizon. We identify the relevant correlation lines in momentum space and compute the intensity of the corresponding signal. We consider a set of different experimental procedures and identify the specific issues of each measuring process. We show that some inter-channel correlations, in particular the Hawking quantum-partner one, are particularly well adapted for witnessing quantum non-separability, being resilient to the effects of temperature and/or quantum quenches.

- 1. LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Momentum distribution and coherence of a weakly interacting Bose gas after a quench

### Giovanni I. Martone

^{1}Pierre-Elie Larré^{2}Alessandro Fabbri^{3}Nicolas Pavloff^{1}*Phys.Rev.A*, 2018, 98 (6), pp.063617. 〈10.1103/PhysRevA.98.063617〉We consider a weakly interacting uniform atomic Bose gas with a time-dependent nonlinear coupling constant. By developing a suitable Bogoliubov treatment we investigate the time evolution of several observables, including the momentum distribution, the degree of coherence in the system, and their dependence on dimensionality and temperature. We rigorously prove that the low-momentum Bogoliubov modes remain frozen during the whole evolution, while the high-momentum ones adiabatically follow the change in time of the interaction strength. At intermediate momenta we point out the occurrence of oscillations, which are analogous to Sakharov oscillations. We identify two wide classes of time-dependent behaviors of the coupling for which an exact solution of the problem can be found, allowing for an analytic computation of all the relevant observables. A special emphasis is put on the study of the coherence property of the system in one spatial dimension. We show that the system exhibits a smooth “light-cone effect,” with typically no prethermalization.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTM - Laboratoire de Physique Théorique et Modélisation
- 3. LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]

## Archive ouverte HAL – Multicritical Edge Statistics for the Momenta of Fermions in Nonharmonic Traps

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Gregory Schehr^{2}Pierre Le Doussal^{1}Satya Majumdar^{2}*Physical Review Letters*, American Physical Society, 2018, 121 (3), 〈10.1103/PhysRevLett.121.030603〉We compute the joint statistics of the momenta $p_i$ of $N$ non-interacting fermions in a trap, near the Fermi edge, with a particular focus on the largest one $p_{\max}$. For a $1d$ harmonic trap, momenta and positions play a symmetric role and hence, the joint statistics of momenta is identical to that of the positions. In particular, $p_{\max}$, as $x_{\max}$, is distributed according to the Tracy-Widom distribution. Here we show that novel "momentum edge statistics" emerge when the curvature of the potential vanishes, i.e. for "flat traps" near their minimum, with $V(x) \sim x^{2n}$ and $n>1$. These are based on generalisations of the Airy kernel that we obtain explicitly. The fluctuations of $p_{\max}$ are governed by new universal distributions determined from the $n$-th member of the second Painlev\'e hierarchy of non-linear differential equations, with connections to multicritical random matrix models. Finite temperature extensions and possible experimental signatures in cold atoms are discussed.

- 1. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Negative Differential Mobility in Interacting Particle Systems

### Amit Kumar Chatterjee

^{1}Urna Basu^{2}P. K. Mohanty^{1}*Physical Review E*, American Physical Society (APS), 2018Driven particles in presence of crowded environment, obstacles or kinetic constraints often exhibit negative differential mobility (NDM) due to their decreased dynamical activity. We propose a new mechanism for complex many-particle systems where slowing down of certain {\it non-driven} degrees of freedom by the external field can give rise to NDM. This phenomenon, resulting from inter-particle interactions, is illustrated in a pedagogical example of two interacting random walkers, one of which is biased by an external field while the same field only slows down the other keeping it unbiased. We also introduce and solve exactly the steady state of several driven diffusive systems, including a two species exclusion model, asymmetric misanthrope and zero-range processes, to show explicitly that this mechanism indeed leads to NDM.

- 1. Saha Institute of Nuclear Physics
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Non-interacting fermions in hard-edge potentials

### Bertrand Lacroix-A-Chez-Toine

^{1}Pierre Le Doussal^{2}Satya Majumdar^{1}Gregory Schehr^{1}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2018, 2018 (12), pp.123103. 〈10.1088/1742-5468/aaeda0〉We consider the spatial quantum and thermal fluctuations of non-interacting Fermi gases of $N$ particles confined in $d$-dimensional non-smooth potentials. We first present a thorough study of the spherically symmetric pure hard-box potential, with vanishing potential inside the box, both at $T=0$ and $T>0$. We find that the correlations near the wall are described by a "hard edge" kernel, which depend both on $d$ and $T$, and which is different from the "soft edge" Airy kernel, and its higher $d$ generalizations, found for smooth potentials. We extend these results to the case where the potential is non-uniform inside the box, and find that there exists a family of kernels which interpolate between the above "hard edge" kernel and the "soft edge" kernels. Finally, we consider one-dimensional singular potentials of the form $V(x)\sim |x|^{-\gamma}$ with $\gamma>0$. We show that the correlations close to the singularity at $x=0$ are described by this "hard edge" kernel for $1\leq\gamma<2$ while they are described by a broader family of "hard edge" kernels known as the Bessel kernel for $\gamma=2$ and, finally by the Airy kernel for $\gamma>2$. These one-dimensional kernels also appear in random matrix theory, and we provide here the mapping between the $1d$ fermion models and the corresponding random matrix ensembles. Part of these results were announced in a recent Letter, EPL 120, 10006 (2017).

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Archive ouverte HAL – Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry

### Christophe Texier

^{1, 2}Johannes Mitscherling^{1, 3}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 〈10.02214〉We study the non-linear conductance $\mathcal{G}\sim\partial^2I/\partial V^2|_{V=0}$ in coherent quasi-1D weakly disordered metallic wires. The analysis is based on the calculation of two fundamental correlators (correlations of conductance's functional derivatives and correlations of injectivities), which are obtained explicitly by using diagrammatic techniques. In a coherent wire of length $L$, we obtain $\mathcal{G}\sim0.006\,E_\mathrm{Th}^{-1}$ (and $\langle\mathcal{G}\rangle=0$), where $E_\mathrm{Th}=D/L^2$ is the Thouless energy and $D$ the diffusion constant; the small dimensionless factor results from screening, i.e. cannot be obtained within a simple theory for non-interacting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal: the antisymmetric part of the non-linear conductance (at high magnetic field) being much smaller than the symmetric one, $\mathcal{G}_a\sim0.001\,(gE_\mathrm{Th})^{-1}$, where $g\gg1$ is the dimensionless (linear) conductance of the wire. Weakly coherent regimes are also studied: for $L_\varphi\ll L$, where $L_\varphi$ is the phase coherence length, we get $\mathcal{G}\sim(L_\varphi/L)^{7/2}E_\mathrm{Th}^{-1}$, and $\mathcal{G}_a\sim(L_\varphi/L)^{11/2}(gE_\mathrm{Th})^{-1}\ll\mathcal{G}$ (at high magnetic field). When thermal fluctuations are important, $L_T\ll L_\varphi\ll L$ where $L_T=\sqrt{D/T}$, we obtain $\mathcal{G}\sim(L_T/L)(L_\varphi/L)^{7/2}E_\mathrm{Th}^{-1}$ (the result is dominated by the effect of screening) and $\mathcal{G}_a\sim(L_T/L)^2(L_\varphi/L)^{7/2}(gE_\mathrm{Th})^{-1}$. All the precise dimensionless prefactors are obtained. Crossovers towards the zero magnetic field regime are also analysed.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides
- 3. Max Planck Institute for Solid State Research

## Archive ouverte HAL – Nontopological parafermions in a one-dimensional fermionic model with even multiplet pairing

### Leonardo Mazza

^{1, 2}Fernando IeminiMarcello DalmonteChristophe Mora^{3}*Phys.Rev.B*, 2018, 98 (20), pp.201109. 〈10.1103/PhysRevB.98.201109〉We discuss a one-dimensional fermionic model with a generalized ZN even multiplet pairing extending Kitaev Z2 chain. The system shares many features with models believed to host localized edge parafermions, the most prominent being a similar bosonized Hamiltonian and a ZN symmetry enforcing an N-fold degenerate ground state robust to certain disorders. Interestingly, we show that the system supports a pair of parafermions but they are nonlocal instead of being boundary operators. As a result, the degeneracy of the ground state is only partly topological and coexists with spontaneous symmetry breaking by a (two-particle) pairing field. Each symmetry-breaking sector is shown to possess a pair of Majorana edge modes encoding the topological twofold degeneracy. Surrounded by two band insulators, the model exhibits for N=4 the dual of an 8π fractional Josephson effect highlighting the presence of parafermions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. FRDPENS - Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris
- 3. LPA - Laboratoire Pierre Aigrain

## Archive ouverte HAL – Notes on the solutions of Zamolodchikov-type recursion relations in Virasoro minimal models

### Nina Javerzat

^{1}Raoul Santachiara^{1}Omar Foda*JHEP*, 2018, 08, pp.183. 〈10.1007/JHEP08(2018)183〉We study Virasoro minimal-model 4-point conformal blocks on the sphere and 0-point conformal blocks on the torus (the Virasoro characters), as solutions of Zamolodchikov-type recursion relations. In particular, we study the singularities due to resonances of the dimensions of conformal fields in minimal-model representations, that appear in the intermediate steps of solving the recursion relations, but cancel in the final results.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – On characteristic polynomials for a generalized chiral random matrix ensemble with a source

### Yan FyodorovJacek Grela

^{1}Eugene Strahov*J.Phys.A*, 2018, 51 (13), pp.134003. 〈10.1088/1751-8121/aaae2a〉We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a random matrix taken from a L-deformed chiral Gaussian Unitary Ensemble with an external source Ω. Relation to a recently studied statistics of bi-orthogonal eigenvectors in the complex Ginibre ensemble, see Fyodorov (2017 arXiv:1710.04699), is briefly discussed as a motivation to study asymptotics of these objects in the case of external source proportional to the identity matrix. In particular, for an associated complex bulk/chiral edge scaling regime we retrieve the kernel related to Bessel/Macdonald functions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – One-dimensional three-boson problem with two- and three-body interactions

### G. Guijarro

^{1}A. Pricoupenko^{2, 3}G. E. Astrakharchik^{1}J. Boronat^{1}D. S. Petrov^{2}*Physical Review A*, American Physical Society, 2018, 97 (6), 〈10.1103/PhysRevA.97.061605〉We solve the three-boson problem with contact two- and three-body interactions in one dimension and analytically calculate the ground and excited trimer-state energies. Then, by using the diffusion Monte Carlo technique we calculate the binding energy of three dimers formed in a one-dimensional Bose-Bose or Fermi-Bose mixture with attractive interspecies and repulsive intraspecies interactions. Combining these results with our three-body analytics we extract the three-dimer scattering length close to the dimer-dimer zero crossing. In both considered cases the three-dimer interaction turns out to be repulsive. Our results constitute a concrete proposal for obtaining a one-dimensional gas with a pure three-body repulsion.

- 1. UPC - Universitat Politècnica de Catalunya [Barcelona]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. ENS Lyon - École normale supérieure - Lyon

## Archive ouverte HAL – Operator Product Expansion in Liouville Field Theory and Seiberg type transitions in log-correlated Random Energy Models

### Xiangyu CaoPierre Le Doussal

^{1}Alberto Rosso^{2}Raoul Santachiara^{2}*Phys.Rev.E*, 2018, 97 (4), pp.042111. 〈10.1103/PhysRevE.97.042111〉We study transitions in log-correlated random energy models (logREMs) that are related to the violation of a Seiberg bound in Liouville field theory (LFT): the binding transition and the termination point transition (a.k.a., pre-freezing). By means of LFT-logREM mapping, replica symmetry breaking and traveling-wave equation techniques, we unify both transitions in a two-parameter diagram, which describes the free-energy large deviations of logREMs with a deterministic background log potential, or equivalently, the joint moments of the free energy and Gibbs measure in logREMs without background potential. Under the LFT-logREM mapping, the transitions correspond to the competition of discrete and continuous terms in a four-point correlation function. Our results provide a statistical interpretation of a peculiar nonlocality of the operator product expansion in LFT. The results are rederived by a traveling-wave equation calculation, which shows that the features of LFT responsible for the transitions are reproduced in a simple model of diffusion with absorption. We examine also the problem by a replica symmetry breaking analysis. It complements the previous methods and reveals a rich large deviation structure of the free energy of logREMs with a deterministic background log potential. Many results are verified in the integrable circular logREM, by a replica-Coulomb gas integral approach. The related problem of common length (overlap) distribution is also considered. We provide a traveling-wave equation derivation of the LFT predictions announced in a precedent work.

- 1. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Orientation of plastic rearrangements in two-dimensional model glasses under shear

### Alexandre Nicolas

^{1}Jörg Rottler^{2}*Physical Review E : Statistical, Nonlinear, and Soft Matter Physics*, American Physical Society, 2018, 97, pp.063002. 〈https://journals.aps.org/pre/pdf/10.1103/PhysRevE.97.063002〉- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. UBC - University of British Columbia

## Archive ouverte HAL – Origins and diagnostics of the nonequilibrium character of active systems

### Lokrshi Prawar Dadhichi

^{1}Ananyo Maitra^{2}Sriram Ramaswamy^{3}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2018We present in detail a Langevin formalism for constructing stochastic dynamical equations for active-matter systems coupled to a thermal bath. We apply the formalism to clarify issues of principle regarding the sources and signatures of nonequilibrium behaviour in a variety of polar and apolar single-particle systems and polar flocks. We show that distance from thermal equilibrium depends on how time-reversal is implemented and hence on the reference equilibrium state. We predict characteristic forms for the frequency-resolved entropy production for an active polar particle in a harmonic potential, which should be testable in experiments.

- 1. TIFR - Tata Institute of Fundamental Research [Hyderabad]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. IISc Bangalore - Indian Institute of Science [Bangalore]

## Archive ouverte HAL – Phase-space study of surface-electrode Paul traps: Integrable, chaotic, and mixed motions

### V. Roberdel

^{1}D. Leibfried^{2}D. Ullmo^{1}H. Landa^{1, 3}*Physical Review A*, American Physical Society, 2018, 97 (5), 〈10.1103/PhysRevA.97.053419〉We present a comprehensive phase-space treatment of the motion of charged particles in electrodynamic traps. Focusing on five-wire surface-electrode Paul traps, we study the details of integrable and chaotic motion of a single ion. We introduce appropriate phase-space measures and give a universal characterization of the trap effectiveness as a function of the parameters. We rigorously derive the commonly used (time-independent) pseudopotential approximation, quantify its regime of validity and analyze the mechanism of its breakdown within the time-dependent potential. The phase space approach that we develop gives a general framework for describing ion dynamics in a broad variety of surface Paul traps. To probe this framework experimentally, we propose and analyze, using numerical simulations, an experiment that can be realized with an existing four-wire trap. We predict a robust experimental signature of the existence of trapping pockets within a mixed regular and chaotic phase-space structure. Intricately rich escape dynamics suggest that surface traps give access to exploring microscopic Hamiltonian transport phenomena in phase space.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. NIST - National Institute of Standards and Technologies
- 3. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Archive ouverte HAL – Pinning by rare defects and effective mobility for elastic interfaces in high dimensions

### Xiangyu Cao

^{1}Vincent Démery^{2, 3}Alberto Rosso^{4, 5}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2018, 51 (23), 〈10.1088/1751-8121/aac02f〉The existence of a depinning transition for a high dimensional interface in a weakly disordered medium is controversial. Following Larkin arguments and a perturbative expansion, one expects a linear response with a renormalized mobility ${\mu}_{\text{eff}}$ . In this paper, we compare these predictions with the exact solution of a fully connected model, which displays a finite critical force $f_c$. At small disorder, we unveil an intermediary linear regime for $f_c < f < 1$ characterized by the renormalized mobility ${\mu}_{\text{eff}}$. Our results suggest that in high dimension the critical force is always finite and determined by the effect of rare impurities that is missed by the perturbative expansion. However, the perturbative expansion correctly describes an intermediate regime that should be visible at small disorder.

- 1. University of California [Berkeley]
- 2. ESPCI - UMR Gulliver
- 3. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. KITP - Kavli Institute for Theoretical Physics

## Archive ouverte HAL – Planar screening by charge polydisperse counterions

### M. Trulsson

^{1, 2}E. Trizac^{1}L. Samaj^{3}*Journal of Physics: Condensed Matter*, IOP Publishing, 2018, 30 (3), 〈10.1088/1361-648X/aa9a79〉We study how a neutralising cloud of counterions screens the electric field of a uniformly charged planar membrane plate, when the counterions are characterised by a distribution of charges (or valence), $n(q)$. We work out analytically the one-plate and two-plate cases, at the level of non-linear Poisson-Boltzmann theory. The (essentially asymptotic) predictions are successfully compared to numerical solutions of the full Poisson-Boltzmann theory, but also to Monte Carlo simulations. The counterions with smallest valence control the long-distance features of interactions, and may qualitatively change the results pertaining to the classic monodisperse case where all counterions have the same charge. Emphasis is put on continuous distributions $n(q)$, for which new power-laws can be evidenced, be it for the ionic density or the pressure, in the one- and two-plates situations respectively. We show that for discrete distributions, more relevant for experiments, these scaling laws persist in an intermediate but yet observable range. Furthermore, it appears that from a practical point of view, hallmarks of the continuous $n(q)$ behaviour is already featured by discrete mixtures with a relatively small number of constituents.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Lund University [Lund]
- 3. Institute of Physics

## Archive ouverte HAL – Post-Ehrenfest many-body quantum interferences in ultracold atoms far out of equilibrium

### Steven Tomsovic

^{1, 2}Peter Schlagheck^{3}Denis Ullmo^{4}Juan Diego Urbina^{1}Klaus Richter^{1}Juan-Diego Urbina*Physical Review A*, American Physical Society, 2018, 97 (6), 〈10.1103/PhysRevA.97.061606〉Far out-of-equilibrium many-body quantum dynamics in isolated systems necessarily generate interferences beyond an Ehrenfest time scale, where quantum and classical expectation values diverge. Of great recent interest is the role these interferences play in the spreading of quantum information across the many degrees of freedom, i.e.~scrambling. Ultracold atomic gases provide a promising setting to explore these phenomena. Theoretically speaking, the heavily-relied-upon truncated Wigner approximation leaves out these interferences. We develop a semiclassical theory which bridges classical and quantum concepts in many-body bosonic systems and properly incorporates such missing quantum effects. For mesoscopically populated Bose-Hubbard systems, it is shown that this theory captures post-Ehrenfest quantum interference phenomena very accurately, and contains relevant phase information to perform many-body spectroscopy with high precision.

- 1. UR - Universität Regensburg
- 2. WSU - Washington State University
- 3. ULg - Institut de Physique
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Power-law random banded matrices and ultrametric matrices: Eigenvector distribution in the intermediate regime

### Eugene Bogomolny

^{1}Martin Sieber^{2}*Physical Review E*, American Physical Society (APS), 2018- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of Bristol [Bristol]

## Archive ouverte HAL – Quantum dynamics with stochastic reset

### B. Mukherjee

^{1}K. Sengupta^{1}Satya N. Majumdar^{2}Satya Majumdar^{2}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 98 (10), 〈10.1103/PhysRevB.98.104309〉We study non-equilibrium dynamics of integrable and non-integrable closed quantum systems whose unitary evolution is interrupted with stochastic resets, characterized by a reset rate $r$, that project the system to its initial state. We show that the steady state density matrix of a non-integrable system, averaged over the reset distribution, retains its off-diagonal elements for any finite $r$. Consequently a generic observable $\hat O$, whose expectation value receives contribution from these off-diagonal elements, never thermalizes under such dynamics for any finite $r$. We demonstrate this phenomenon by exact numerical studies of experimentally realizable models of ultracold bosonic atoms in a tilted optical lattice. For integrable Dirac-like fermionic models driven periodically between such resets, the reset-averaged steady state is found to be described by a family of generalized Gibbs ensembles (GGE s) characterized by $r$. We also study the spread of particle density of a non-interacting one-dimensional fermionic chain, starting from an initial state where all fermions occupy the left half of the sample, while the right half is empty. When driven by resetting dynamics, the density profile approaches at long times to a nonequilibrium stationary profile that we compute exactly. We suggest concrete experiments that can possibly test our theory.

- 1. Indian Association for the Cultivation of Sciences
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Quantum purification spectroscopy

### Bradraj Pandey

^{1}Kirill Plekhanov^{1, 2}Guillaume Roux^{1}*Phys.Rev.A*, 2018, 98 (5), pp.050103. 〈10.1103/PhysRevA.98.050103〉We discuss a protocol based on quenching a purified quantum system that allows one to capture bulk spectral features. It uses an infinite temperature initial state and an interferometric strategy to access the Loschmidt amplitude, from which the spectral features are retrieved via Fourier transform, providing coarse-grained approximation at finite times. It involves techniques available in current experimental setups for quantum simulation, at least for small systems. We illustrate possible applications in testing the eigenstate thermalization hypothesis and the physics of many-body localization.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. CPHT - Centre de Physique Théorique [Palaiseau]

## Archive ouverte HAL – Reaction kinetics of ultracold molecule-molecule collisions

### Daniel K. Hoffmann

^{1}Thomas Paintner^{1}Wolfgang Limmer^{1}Dmitry S. Petrov^{2}Johannes Hecker Denschlag^{1}*Nature Communications*, Nature Publishing Group, 2018Studying chemical reactions on a state-to-state level tests and improves our fundamental understanding of chemical processes. For such investigations it is convenient to make use of ultracold atomic and molecular reactants as they can be prepared in well defined internal and external quantum states$^{1-4}$. In general, even cold reactions have many possible final product states$^{5-15}$ and reaction channels are therefore hard to track individually$^{16}$. In special cases, however, only a single reaction channel is essentially participating, as observed e.g. in the recombination of two atoms forming a Feshbach molecule$^{17-19}$ or in atom-Feshbach molecule exchange reactions$^{20,21}$. Here, we investigate a single-channel reaction of two Li$_2$-Feshbach molecules where one of the molecules dissociates into two atoms $2\mathrm{AB}\Rightarrow \mathrm{AB}+\mathrm{A}+\mathrm{B}$. The process is a prototype for a class of four-body collisions where two reactants produce three product particles. We measure the collisional dissociation rate constant of this process as a function of collision energy/ temperature and scattering length. We confirm an Arrhenius-law dependence on the collision energy, an $a^4$ power-law dependence on the scattering length $a$ and determine a universal four body reaction constant.

- 1. Ulm University
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Responses to auxin signals: an operating principle for dynamical sensitivity yet high resilience

### Silvia Grigolon

^{1}Barbara Bravi^{2}Olivier C. Martin^{1, 3}*Royal Society Open Science*, The Royal Society, 2018, 5 (1), 〈10.1098/rsos.172098〉Plants depend on the signaling of the phytohormone auxin for their development and for responding to environmental perturbations. The associated biomolecular signaling network involves a negative feedback at the level of the Aux/IAA proteins which mediate the influence of auxin (the signal) on the ARF transcription factors (the drivers of the response). To probe the role of this feedback, we consider alternative in silico signaling networks implementing different operating principles. By a comparative analysis, we find that the presence of a negative regulatory feedback loop allows the system to have a far larger sensitivity in its dynamical response to auxin. At the same time, this sensitivity does not prevent the system from being highly resilient. Given this insight, we reconsider previously published models and build a new quantitative and calibrated biomolecular model of auxin signaling.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. King‘s College London
- 3. GQE-Le Moulon - Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale)

## Archive ouverte HAL – Role of City Texture in Urban Heat Islands at Nighttime

### J.M. SobstylT. Emig

^{1}M.J. Abdolhosseini QomiF.-J. UlmRoland J.-M. Pellenq^{2, 3}*Phys.Rev.Lett.*, 2018, 120 (10), pp.108701. 〈10.1103/PhysRevLett.120.108701〉An urban heat island (UHI) is a climate phenomenon that results in an increased air temperature in cities when compared to their rural surroundings. In this Letter, the dependence of an UHI on urban geometry is studied. Multiyear urban-rural temperature differences and building footprints data combined with a heat radiation scaling model are used to demonstrate for more than 50 cities worldwide that city texture—measured by a building distribution function and the sky view factor—explains city-to-city variations in nocturnal UHIs. Our results show a strong correlation between nocturnal UHIs and the city texture.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. MIT - Massachusetts Institute of Technology
- 3. CINaM - Centre Interdisciplinaire de Nanoscience de Marseille

## Archive ouverte HAL – Run and tumble particle under resetting: a renewal approach

### Martin R. Evans

^{1}Satya N. Majumdar^{2}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2018, 51 (47), pp.475003. 〈10.1088/1751-8121/aae74e〉We consider a particle undergoing run and tumble dynamics, in which its velocity stochastically reverses, in one dimension. We study the addition of a Poissonian resetting process occurring with rate $r$. At a reset event the particle's position is returned to the resetting site $X_r$ and the particle's velocity is reversed with probability $\eta$. The case $\eta = 1/2$ corresponds to position resetting and velocity randomization whereas $\eta =0$ corresponds to position-only resetting. We show that, beginning from symmetric initial conditions, the stationary state does not depend on $\eta$ i.e. it is independent of the velocity resetting protocol. However, in the presence of an absorbing boundary at the origin, the survival probability and mean time to absorption do depend on the velocity resetting protocol. Using a renewal equation approach, we show that the the mean time to absorption is always less for velocity randomization than for position-only resetting.

- 1. SUPA, School of Physics, University of Edinburgh
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Separating intrinsic interactions from extrinsic correlations in a network of sensory neurons

### Ulisse Ferrari

^{1}Stéphane Deny^{2}Matthew Chalk^{1}Gašper Tkačik^{3}Olivier Marre^{1}Thierry Mora^{4}*Physical Review E*, American Physical Society (APS), 2018, 98 (4), pp.042410. 〈10.1103/PhysRevE.98.042410〉Correlations in sensory neural networks have both extrinsic and intrinsic origins. Extrinsic or stimulus correlations arise from shared inputs to the network and, thus, depend strongly on the stimulus ensemble. Intrinsic or noise correlations reflect biophysical mechanisms of interactions between neurons, which are expected to be robust to changes in the stimulus ensemble. Despite the importance of this distinction for understanding how sensory networks encode information collectively, no method exists to reliably separate intrinsic interactions from extrinsic correlations in neural activity data, limiting our ability to build predictive models of the network response. In this paper we introduce a general strategy to infer population models of interacting neurons that collectively encode stimulus information. The key to disentangling intrinsic from extrinsic correlations is to infer the couplings between neurons separately from the encoding model and to combine the two using corrections calculated in a mean-field approximation. We demonstrate the effectiveness of this approach in retinal recordings. The same coupling network is inferred from responses to radically different stimulus ensembles, showing that these couplings indeed reflect stimulus-independent interactions between neurons. The inferred model predicts accurately the collective response of retinal ganglion cell populations as a function of the stimulus.

- 1. Institut de la Vision
- 2. Stanford University [Stanford]
- 3. IST - Institute of Science and Technology Austria [Klosterneuburg, Austria]
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Singularities of Floquet scattering and tunneling

### H. Landa

^{1, 2}*Physical Review A*, American Physical Society, 2018, 97 (4), 〈10.1103/PhysRevA.97.042705〉We study quasi-bound states and scattering with short range potentials in three dimensions, subject to an axial periodic driving. We find that poles of the scattering S-matrix can cross the real energy axis as a function of the drive amplitude, making the S-matrix nonanalytic at a singular point. For the corresponding quasi-bound states that can tunnel out of (or get captured within) a potential well, this results in a discontinuous jump in both the angular momentum and energy of emitted (absorbed) waves. We also analyze elastic and inelastic scattering of slow particles in the time dependent potential. For a drive amplitude at the singular point, there is a total absorption of incoming low energy (s-wave) particles and their conversion to high energy outgoing (mostly p-) waves. We examine the relation of such Floquet singularities, lacking in an effective time independent approximation, with well known "spectral singularities" (or "exceptional points"). These results are based on an analytic approach for obtaining eigensolutions of time-dependent periodic Hamiltonians with mixed cylindrical and spherical symmetry, and apply broadly to particles interacting via power law forces and subject to periodic fields, e.g. co-trapped ions and atoms.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Archive ouverte HAL – Soft modes and strain redistribution in continuous models of amorphous plasticity: the Eshelby paradigm, and beyond?

### Xiangyu Cao

^{1, 2}Alexandre Nicolas^{1}Denny Trimcev^{1, 3}Alberto Rosso^{1}*Soft Matter*, Royal Society of Chemistry, 2018, 14 (18), pp.3640 - 3651. 〈10.1039/C7SM02510F〉The deformation of disordered solids relies on swift and localised rearrangements of particles. The inspection of soft vibrational modes can help predict the locations of these rearrangements, while the strain that they actually redistribute mediates collective effects. Here, we study soft modes and strain redistribution in a two-dimensional continuous mesoscopic model based on a Ginzburg-Landau free energy for perfect solids, supplemented with a plastic disorder potential that accounts for shear softening and rearrangements. Regardless of the disorder strength, our numerical simulations show soft modes that are always sharply peaked at the softest point of the material (unlike what happens for the depinning of an elastic interface). Contrary to widespread views, the deformation halo around this peak does not always have a quadrupolar (Eshelby-like) shape. Instead, for finite and narrowly-distributed disorder, it looks like a fracture, with a strain field that concentrates along some easy directions. These findings are rationalised with analytical calculations in the case where the plastic disorder is confined to a point-like `impurity'. In this case, we unveil a continuous family of elastic propagators, which are identical for the soft modes and for the equilibrium configurations. This family interpolates between the standard quadrupolar propagator and the fracture-like one as the anisotropy of the elastic medium is increased. Therefore, we expect to see a fracture-like propagator when extended regions on the brink of failure have already softened along the shear direction and thus rendered the material anisotropic, but not failed yet. We speculate that this might be the case in carefully aged glasses just before macroscopic failure.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of California [Berkeley]
- 3. ENS Paris - École normale supérieure - Paris

## Archive ouverte HAL – Something interacting and solvable in 1D

### Eyzo StoutenPieter W. ClaeysMikhail Zvonarev

^{1}Jean-Sébastien CauxVladimir Gritsev*J.Phys.A*, 2018, 51 (48), pp.485204. 〈10.1088/1751-8121/aae8bb〉We present a two-parameter family of exactly solvable quantum many-body systems in one spatial dimension containing the Lieb–Liniger model of interacting bosons as a particular case. The principal building block of this construction is the previously-introduced (Stouten et al 2018 arXiv:1712.09375) family of two-particle scattering matrices. We discuss an transformation connecting the models within this family and make a correspondence with generalized point interactions. The Bethe equations for the ground state are discussed with a special emphasis on ‘non-interacting modes’ connected by the modular subgroup of . The bound state solutions are discussed and are conjectured to follow some correlated version of the string hypothesis. The excitation spectrum of the new models in this family is derived in analogy to the Lieb–Liniger model and we show that for certain choices of parameters a spectrum inversion occurs such that the Umklapp solutions become the new ground state.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Spectral content of fractional Brownian motion with stochastic reset

### Satya N Majumdar

^{1}Gleb Oshanin^{2}Satya Majumdar^{1}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2018, 51 (43), 〈10.1088/1751-8121/aadef0〉We analyse the power spectral density (PSD) $S_T(f)$ (with $T$ being the observation time and $f$ is the frequency) of a fractional Brownian motion (fBm), with an arbitrary Hurst index $H \in (0,1)$, undergoing a stochastic resetting to the origin at a constant rate $r$ - the resetting process introduced some time ago as an example of an efficient, optimisable search algorithm. To this end, we first derive an exact expression for the covariance function of an arbitrary (not necessarily a fBm) process with a reset, expressing it through the covariance function of the parental process without a reset, which yields the desired result for the fBm in a particular case. We then use this result to compute exactly the power spectral density for fBM for all frequency $f$. The asymptotic, large frequency $f$ behaviour of the PSD turns out to be distinctly different for sub- $(H < 1/2)$ and super-diffusive $(H > 1/2)$ fBms. We show that for large $f$, the PSD has a power law tail: $S_T(f) \sim 1/f^{\gamma}$ where the exponent $\gamma= 2H+1$ for $0

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

## Archive ouverte HAL – Stable $p$-wave resonant two-dimensional Fermi-Bose dimers

### Betzalel BazakDmitry S. Petrov

^{1}*Phys.Rev.Lett.*, 2018, 121, pp.263001. 〈10.1103/PhysRevLett.121.263001〉We consider two-dimensional weakly-bound heterospecies molecules formed in a Fermi-Bose mixture with attractive Fermi-Bose and repulsive Bose-Bose interactions. Bosonic exchanges lead to an intermolecular attraction, which can be controlled and tuned to a p-wave resonance. Such attractive fermionic molecules can be realized in quasi-two-dimensional ultracold isotopic or heteronuclear mixtures. We show that they are stable with respect to the recombination to deeply-bound molecular states and with respect to the formation of higher-order clusters (trimers, tetramers, etc.)

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

### Kanaya Malakar

^{1}V. Jemseena^{2}Anupam Kundu^{2}K. Vijay Kumar^{2}Sanjib Sabhapandit^{3}Satya N. Majumdar^{4}S. Redner^{5}Abhishek Dhar^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2018We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verifications of our analytical results.

- 1. Presidency University
- 2. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
- 3. Raman Research Institute
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Santa Fe Institute

## Archive ouverte HAL – Strong-coupling theory of counterions between symmetrically charged walls: from crystal to fluid phases

### L. Samaj

^{1}M. Trulsson^{2}E. Trizac^{3}*Soft Matter*, Royal Society of Chemistry, 2018We study thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance $d$. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle deviations is made around the bilayer positions, with a free lattice parameter determined from a variational approach. For each of the two walls, the harmonic expansion implies an effective one-body potential at the root of all observables of interest in our Wigner Strong-Coupling expansion. Analytical results for the particle density profile and the pressure are in good agreement with numerical Monte Carlo data, for small as well as intermediate values of $d$ comparable with the Wigner lattice spacing. While the strong-coupling theory is extended to the fluid regime by using the concept of a correlation hole, the Wigner calculations appear trustworthy for all electrostatic couplings investigated. Our results significantly extend the range of accuracy of analytical equations of state for strongly interacting charged planar interfaces.

- 1. Institute of Physics
- 2. Lund University [Lund]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Superfluidity of identical fermions in an optical lattice: Atoms and polar molecules

### A. K. Fedorov

^{1}V. I. Yudson^{2}G. V. Shlyapnikov^{3, 4, 1}*AIP Conference Proceedings*, American Institute of Physics, 2018, 〈10.1063/1.5025460〉In this work, we discuss the emergence of $p$-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices, for short-range interacting atoms, the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the $p$-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create atomic $p$-wave superfluids with sizable transition temperatures. The situation is drastically different for fermionic polar molecules. Being dressed with a microwave field, they acquire a dipole-dipole attractive tail in the interaction potential. Then, due to a long-range character of the dipole-dipole interaction, the effect of the suppression of the scattering amplitude in 2D lattices is absent. This leads to the emergence of a stable topological $p_x+ip_y$ superfluid of identical microwave-dressed polar molecules.

- 1. Russian Quantum Center
- 2. Institute of Spectroscopy
- 3. Wuhan Institute of Physics and Mathematics
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Surface temperatures in New York City: Geospatial data enables the accurate prediction of radiative heat transfer

### Masoud Ghandehari

^{1}Thorsten Emig^{2, 3}Milad Aghamohamadnia^{1}*Scientific Reports*, Nature Publishing Group, 2018Three decades into the research seeking to derive the urban energy budget, the dynamics of the thermal exchange between the densely built infrastructure and the environment are still not well understood. We present a novel hybrid experimental-numerical approach for the analysis of the radiative heat transfer in New York City. The aim of this work is to contribute to the calculation of the urban energy budget, in particular the stored energy. Improved understanding of urban thermodynamics incorporating the interaction of the various bodies will have implications on energy conservation at the building scale, as well as human health and comfort at the urban scale. The platform presented is based on longwave hyperspectral imaging of nearly 100 blocks of Manhattan, and a geospatial radiosity model that describes the collective radiative heat exchange between multiple buildings. The close comparison of temperature values derived from measurements and the computed surface temperatures (including streets and roads) implies that this geospatial, thermodynamic numerical model applied to urban structures, is promising for accurate and high resolution analysis of urban surface temperatures.

- 1. NYU Tandon School of Engineering
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. MSE2 - Multiscale Materials Science for Energy and Environment

## Archive ouverte HAL – The impact of the injection protocol on an impurity’s stationary state

### Oleksandr Gamayun

^{1, 2}Oleg Lychkovskiy^{3, 4, 5}Evgeni Burovski^{6, 7}Matthew Malcomson^{8}Vadim V. Cheianov^{1}Mikhail B. Zvonarev^{9}*Physical Review Letters*, American Physical Society, 2018We examine stationary state properties of an impurity particle injected into a one-dimensional quantum gas. We show that the value of the impurity's end velocity lies between zero and the speed of sound in the gas, and is determined by the injection protocol. This way, the impurity's constant motion is a dynamically emergent phenomenon whose description goes beyond accounting for the kinematic constraints of Landau approach to superfluidity. We provide exact analytic results in the thermodynamic limit, and perform finite-size numerical simulations to demonstrate that the predicted phenomena are within the reach of the existing ultracold gases experiments.

- 1. Universiteit Leiden [Leiden]
- 2. Bogolyubov Institute for Theoretical Physics
- 3. Skoltech - Skolkovo Institute of Science and Technology [Moscow]
- 4. Steklov Mathematical Institute of Russian Academy of Sciences
- 5. Russian Quantum Center
- 6. National Research University Higher School of Economics [Moscow]
- 7. Science Center in Chernogolovka
- 8. Lancaster University
- 9. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – The open XXZ spin chain in the SoV framework: scalar product of separate states

### N. Kitanine

^{1}J.M. Maillet^{2}G. Niccoli^{2}V. Terras^{3}*J.Phys.A*, 2018, 51 (48), pp.485201. 〈10.1088/1751-8121/aae76f〉In our previous paper (Kitanine et al 2017 J. Phys. A: Math. Theor. 50 224001) we have obtained, for the XXX spin-1/2 Heisenberg open chain, new determinant representations for the scalar products of separate states in the quantum separation of variables (SoV) framework. In this article we perform a similar study in a more complicated case: the XXZ open spin-1/2 chain with the most general integrable boundary terms. We first revisit the SoV solution of this model using a matrix version of the Vertex-IRF gauge transformation so as to reduce one of the boundary K-matrices to a diagonal form. As usual within the SoV approach, the scalar products of separate states are computed in terms of dressed Vandermonde determinants having an intricate dependency on the inhomogeneity parameters. We show that these determinants can be transformed into different ones in which the homogeneous limit can be taken straightforwardly. These representations generalize in a non-trivial manner to the trigonometric case the expressions found previously in the rational case. We also show that generically all scalar products can be expressed in a form which is similar to—although more cumbersome than—the well-known Slavnov determinant representation for the scalar products of the Bethe states of the periodic chain. Considering a special choice of the boundary parameters relevant in the thermodynamic limit to describe the half infinite chain with a general boundary, we particularize these representations to the case of one of the two states being an eigenstate. We obtain simplified formulas that should be of direct use to compute the form factors and correlation functions of this model.

- 1. IMB - Institut de Mathématiques de Bourgogne [Dijon]
- 2. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Topological Zak Phase in Strongly-Coupled LC Circuits

### Tal Goren

^{1}Kirill Plekhanov^{1, 2}Félicien Appas^{1}Karyn Le Hur^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018We show the emergence of topological Bogoliubov bosonic excitations in the relatively strong coupling limit of an LC (inductance-capacitance) one-dimensional quantum circuit. This dimerized chain model reveals a ${\cal Z}_2$ local symmetry as a result of the counter-rotating wave (pairing) terms. The topology is protected by the sub-lattice symmetry, represented by an anti-unitary transformation. We present a methos to measure the winding of the topological Zak phase across the Brillouin zone by a reflection measurement of (microwave) light. Our method probes bulk quantities and can be implemented even in small systems. We study the robustness of edge modes towards disorder.

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Topology of Disconnected Elementary Band Representations

### Jennifer Cano

^{1}Barry Bradlyn^{1}Zhijun Wang^{2}L. Elcoro^{3}M. g. Vergniory^{3}C. Felser^{4}M. i. Aroyo^{3}B. Andrei Bernevig^{5, 6, 7}*Physical Review Letters*, American Physical Society, 2018, 120 (26), 〈10.1103/PhysRevLett.120.266401〉Elementary band representations are the fundamental building blocks of atomic limit band structures. They have the defining property that at partial filling they cannot be both gapped and trivial. Here, we give two examples -- one each in a symmorphic and a non-symmorphic space group -- of elementary band representations realized with an energy gap. In doing so, we explicitly construct a counterexample to a claim by Michel and Zak that single-valued elementary band representations in non-symmorphic space groups with time-reversal symmetry are connected. For each example, we construct a topological invariant to explicitly demonstrate that the valence bands are non-trivial. We discover a new topological invariant: a movable but unremovable Dirac cone in the "Wilson Hamiltonian" and a bent-Z2 index.

- 1. Princeton University, Princeton, NJ 08544, USA
- 2. Princeton University
- 3. University of the Basque Country - University of the Basque Country
- 4. CPfS - Max Planck Institute for Chemical Physics of Solids
- 5. DPPU - Department of Physics,Princeton University
- 6. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 7. LPA - Laboratoire Pierre Aigrain

## Archive ouverte HAL – Towards Quantum Simulation with Circular Rydberg Atoms

### Thanh Long Nguyen

^{1}Jean-Michel Raimond^{1}Clément Sayrin^{1}Rodrigo Cortinas^{1}Tigrane Cantat-Moltrecht^{1}Fédéric Assemat^{1}Igor Dotsenko^{1}Sébastien Gleyzes^{1}Serge Haroche^{1}Guillaume Roux^{2}Thierry Jolicoeur^{2}Michel Brune^{1}*Physical Review X*, American Physical Society, 2018, 8 (1), 〈10.1103/PhysRevX.8.011032〉The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic approaches to many-body systems are limited and the huge size of their Hilbert space makes numerical simulations on classical computers intractable. A quantum simulator avoids these limitations by transcribing the system of interest into another, with the same dynamics but with interaction parameters under control and with experimental access to all relevant observables. Quantum simulation of spin systems is being explored with trapped ions, neutral atoms and superconducting devices. We propose here a new paradigm for quantum simulation of spin-1/2 arrays providing unprecedented flexibility and allowing one to explore domains beyond the reach of other platforms. It is based on laser-trapped circular Rydberg atoms. Their long intrinsic lifetimes combined with the inhibition of their microwave spontaneous emission and their low sensitivity to collisions and photoionization make trapping lifetimes in the minute range realistic with state-of-the-art techniques. Ultra-cold defect-free circular atom chains can be prepared by a variant of the evaporative cooling method. This method also leads to the individual detection of arbitrary spin observables. The proposed simulator realizes an XXZ spin-1/2 Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kHz. All the model parameters can be tuned at will, making a large range of simulations accessible. The system evolution can be followed over times in the range of seconds, long enough to be relevant for ground-state adiabatic preparation and for the study of thermalization, disorder or Floquet time crystals. This platform presents unrivaled features for quantum simulation.

- 1. LKB [Collège de France] - Laboratoire Kastler Brossel
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Universality Classes of Interaction Structures for NK Fitness Landscapes

### Sungmin Hwang

^{1, 2}Benjamin Schmiegelt^{2}Luca Ferretti^{3}Joachim Krug^{2}*Journal of Statistical Physics*, Springer Verlag, 2018, 172 (1), pp.226 - 278. 〈10.1007/s10955-018-1979-z〉Kauffman's NK-model is a paradigmatic example of a class of stochastic models of genotypic fitness landscapes that aim to capture generic features of epistatic interactions in multilocus systems. Genotypes are represented as sequences of $L$ binary loci. The fitness assigned to a genotype is a sum of contributions, each of which is a random function defined on a subset of $k \le L$ loci. These subsets or neighborhoods determine the genetic interactions of the model. Whereas earlier work on the NK model suggested that most of its properties are robust with regard to the choice of neighborhoods, recent work has revealed an important and sometimes counter-intuitive influence of the interaction structure on the properties of NK fitness landscapes. Here we review these developments and present new results concerning the number of local fitness maxima and the statistics of selectively accessible (that is, fitness-monotonic) mutational pathways. In particular, we develop a unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of $L$, and identify two different universality classes of interaction structures that display different asymptotics of this quantity for large $k$. Moreover, we show that the probability that the fitness landscape can be traversed along an accessible path decreases exponentially in $L$ for a large class of interaction structures that we characterize as locally bounded. Finally, we discuss the impact of the NK interaction structures on the dynamics of evolution using adaptive walk models.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of Cologne
- 3. The Pirbright Institute

## Archive ouverte HAL – Wigner function of noninteracting trapped fermions

### David Dean

^{1}Pierre Le Doussal^{2}Satya Majumdar^{3}Gregory Schehr^{3}*Physical Review A*, American Physical Society, 2018, 97 (6), pp.063614 (1-14). 〈10.1103/PhysRevA.97.063614〉We study analytically the Wigner function W N (x,p) of N noninteracting fermions trapped in a smooth confining potential V (x) in d dimensions. At zero temperature, W N (x,p) is constant over a finite support in the phase space (x,p) and vanishes outside. Near the edge of this support, we find a universal scaling behavior of W N (x,p) for large N. The associated scaling function is independent of the precise shape of the potential as well as the spatial dimension d. We further generalize our results to finite temperature T > 0. We show that there exists a low-temperature regime T ∼ e N /b, where e N is an energy scale that depends on N and the confining potential V (x), where the Wigner function at the edge again takes a universal scaling form with a b-dependent scaling function. This temperature-dependent scaling function is also independent of the potential as well as the dimension d. Our results generalize to any d 1 and T 0 the d = 1 and T = 0 results obtained by Bettelheim and Wiegman [Phys. Rev. B 84, 085102 (2011)] (see also the earlier paper by Balazs and Zipfel [Ann. Phys. (NY) 77, 139 (1973)]).

- 1. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Wigner–Smith time-delay matrix in chaotic cavities with non-ideal contacts

### Aurélien Grabsch

^{1}Dmitry V. SavinChristophe Texier^{1}*J.Phys.A*, 2018, 51 (40), pp.404001. 〈10.1088/1751-8121/aada43〉We consider wave propagation in a complex structure coupled to a finite number N of scattering channels, such as chaotic cavities or quantum dots with external leads. Temporal aspects of the scattering process are analysed through the concept of time delays, related to the energy (or frequency) derivative of the scattering matrix . We develop a random matrix approach to study the statistical properties of the symmetrised Wigner–Smith time-delay matrix , and obtain the joint distribution of and for the system with non-ideal contacts, characterised by a finite transmission probability (per channel) . We derive two representations of the distribution of in terms of matrix integrals specified by the Dyson symmetry index (the general case of unequally coupled channels is also discussed). We apply this to the Wigner time delay , which is an important quantity providing the density of states of the open system. Using the obtained results, we determine the distribution of the Wigner time delay in the weak coupling limit and identify the following three regimes. (i) The large deviations at small times (measured in units of the Heisenberg time) are characterised by the limiting behaviour for . (ii) The distribution shows the universal behaviour in some intermediate range . (iii) It has a power law decay for large .

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Band connectivity for topological quantum chemistry: Band structures as a graph theory problem

### Barry Bradlyn

^{1}L. Elcoro^{2}M. G. Vergniory^{2}Jennifer Cano^{1}Zhijun Wang^{1}C. Felser^{3}M. I. Aroyo^{2}B. Andrei Bernevig^{4, 5, 6}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 97 (3), 〈10.1103/PhysRevB.97.035138〉The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a recent paper [B. Bradlyn et al., Nature 547, 298 (2017)], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local "k-dot-p" band structures across the Brillouin zone in terms of graph theory. In the current manuscript we give the details of our full theoretical construction. We show that crystal symmetries strongly constrain the allowed connectivities of energy bands, and we employ graph-theoretic techniques such as graph connectivity to enumerate all the solutions to these constraints. The tools of graph theory allow us to identify disconnected groups of bands in these solutions, and so identify topologically distinct insulating phases.

- 1. Princeton University, Princeton, NJ 08544, USA
- 2. University of the Basque Country - University of the Basque Country
- 3. Max Planck Institute for Chemical Physics of Solids
- 4. DPPU - Department of Physics,Princeton University
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. LPA - Laboratoire Pierre Aigrain

## Building blocks of topological quantum chemistry: Elementary band representations

### Jennifer Cano

^{1}Barry Bradlyn^{1}Zhijun Wang^{1}L. Elcoro^{2}M. G. Vergniory^{2}C. Felser^{3}M. I. Aroyo^{2}B. Andrei Bernevig^{4, 5, 6}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 97 (3), 〈10.1103/PhysRevB.97.035139〉The link between chemical orbitals described by local degrees of freedom and band theory, which is defined in momentum space, was proposed by Zak several decades ago for spinless systems with and without time-reversal in his theory of "elementary" band representations. In Nature 547, 298-305 (2017), we introduced the generalization of this theory to the experimentally relevant situation of spin-orbit coupled systems with time-reversal symmetry and proved that all bands that do not transform as band representations are topological. Here, we give the full details of this construction. We prove that elementary band representations are either connected as bands in the Brillouin zone and are described by localized Wannier orbitals respecting the symmetries of the lattice (including time-reversal when applicable), or, if disconnected, describe topological insulators. We then show how to generate a band representation from a particular Wyckoff position and determine which Wyckoff positions generate elementary band representations for all space groups. This theory applies to spinful and spinless systems, in all dimensions, with and without time reversal. We introduce a homotopic notion of equivalence and show that it results in a finer classification of topological phases than approaches based only on the symmetry of wavefunctions at special points in the Brillouin zone. Utilizing a mapping of the band connectivity into a graph theory problem, which we introduced in Nature 547, 298-305 (2017), we show in companion papers which Wyckoff positions can generate disconnected elementary band representations, furnishing a natural avenue for a systematic materials search.

- 1. Princeton University, Princeton, NJ 08544, USA
- 2. University of the Basque Country - University of the Basque Country
- 3. Max Planck Institute for Chemical Physics of Solids
- 4. DPPU - Department of Physics,Princeton University
- 5. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 6. LPA - Laboratoire Pierre Aigrain

## Cell contraction induces long-ranged stress stiffening in the extracellular matrix

### Yu Long Han

^{1}Pierre Ronceray^{2}Guoqiang Xu^{1}Andrea Malandrino^{3, 1}Roger Kamm^{1}Martin Lenz^{4}Chase P. Broedersz^{5}Ming Guo^{1}*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2018Animal cells in tissues are supported by biopolymer matrices, which typically exhibit highly nonlinear mechanical properties. While the linear elasticity of the matrix can significantly impact cell mechanics and functionality, it remains largely unknown how cells, in turn, affect the nonlinear mechanics of their surrounding matrix. Here we show that living contractile cells are able to generate a massive stiffness gradient in three distinct 3D extracellular matrix model systems: collagen, fibrin, and Matrigel. We decipher this remarkable behavior by introducing Nonlinear Stress Inference Microscopy (NSIM), a novel technique to infer stress fields in a 3D matrix from nonlinear microrheology measurement with optical tweezers. Using NSIM and simulations, we reveal a long-ranged propagation of cell-generated stresses resulting from local filament buckling. This slow decay of stress gives rise to the large spatial extent of the observed cell-induced matrix stiffness gradient, which could form a mechanism for mechanical communication between cells.

- 1. MIT - Massachusetts Institute of Technology
- 2. Princeton Center for Theoretical Science
- 3. IBEC - Institute for Bioengineering of Catalonia [Barcelona]
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Ludwig-Maximilians-Universität München

## Closed-Loop Estimation of Retinal Network Sensitivity by Local Empirical Linearization

### Ulisse Ferrari

^{1}Christophe Gardella^{1}Olivier Marre^{1}Thierry Mora^{2}*eNeuro*, Society for Neuroscience, 2018, 4 (6), pp.ENEURO.0166-17.2017. 〈10.1523/ENEURO.0166-17.2017〉Understanding how sensory systems process information depends crucially on identifying which features of the stimulus drive the response of sensory neurons, and which ones leave their response invariant. This task is made difficult by the many nonlinearities that shape sensory processing. Here, we present a novel perturbative approach to understand information processing by sensory neurons, where we linearize their collective response locally in stimulus space. We added small perturbations to reference stimuli and tested if they triggered visible changes in the responses, adapting their amplitude according to the previous responses with closed-loop experiments. We developed a local linear model that accurately predicts the sensitivity of the neural responses to these perturbations. Applying this approach to the rat retina, we estimated the optimal performance of a neural decoder and showed that the nonlinear sensitivity of the retina is consistent with an efficient encoding of stimulus information. Our approach can be used to characterize experimentally the sensitivity of neural systems to external stimuli locally, quantify experimentally the capacity of neural networks to encode sensory information, and relate their activity to behavior.

- 1. Institut de la Vision
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Correlations of occupation numbers in the canonical ensemble and application to a Bose-Einstein condensate in a one-dimensional harmonic trap

### Olivier Giraud

^{1}Aurélien Grabsch^{1}Christophe Texier^{1}*Physical Review A*, American Physical Society, 2018, 97 (5), 〈10.1103/PhysRevA.97.053615〉We study statistical properties of $N$ non-interacting identical bosons or fermions in the canonical ensemble. We derive several general representations for the $p$-point correlation function of occupation numbers $\overline{n_1\cdots n_p}$. We demonstrate that it can be expressed as a ratio of two $p\times p$ determinants involving the (canonical) mean occupations $\overline{n_1}$, ..., $\overline{n_p}$, which can themselves be conveniently expressed in terms of the $k$-body partition functions (with $k\leq N$). We draw some connection with the theory of symmetric functions, and obtain an expression of the correlation function in terms of Schur functions. Our findings are illustrated by revisiting the problem of Bose-Einstein condensation in a 1D harmonic trap, for which we get analytical results. We get the moments of the occupation numbers and the correlation between ground state and excited state occupancies. In the temperature regime dominated by quantum correlations, the distribution of the ground state occupancy is shown to be a truncated Gumbel law. The Gumbel law, describing extreme value statistics, is obtained when the temperature is much smaller than the Bose-Einstein temperature.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Duality in Power-Law Localization in Disordered One-Dimensional Systems

### X. Deng

^{1}V. e. Kravtsov^{2, 3}G. v. Shlyapnikov^{4, 5, 6, 7, 8}L. Santos^{1}*Physical Review Letters*, American Physical Society, 2018, 120 (11), 〈10.1103/PhysRevLett.120.110602〉The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, $1/r^a$. For randomly spaced particles, these models present an effective peculiar disorder that leads to surprising localization properties. We show that in one-dimensional systems almost all eigenstates (except for a few states close to the ground state) are power-law localized for any value of $a>0$. Moreover, we show that our model is an example of a new universality class of models with power-law hopping, characterized by a duality between systems with long-range hops ($a<1$) and short-range hops ($a>1$) in which the wave function amplitude falls off algebraically with the same power $\gamma$ from the localization center.

- 1. LUH - Leibniz Universität Hannover [Hannover]
- 2. ICTP - International Center for Theoretical Physics [Trieste]
- 3. L.D. Landau Institute for Theoretical Physics of RAS
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. SPEC - UMR3680 - Service de physique de l'état condensé
- 6. Russian Quantum Center
- 7. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 8. Wuhan Institute of Physics and Mathematics

## Eigenstate versus Zeeman-based approaches to the solid effect

### Inés Rodríguez-Arias

^{1}Alberto Rosso^{1}Andrea De Luca^{2}*Magnetic Resonance in Chemistry*, Wiley, 2018, 56 (7), pp.689 - 698. 〈10.1002/mrc.4724〉The solid effect is one of the simplest and most effective mechanisms for Dynamic Nuclear Polarization. It involves the exchange of polarization between one electron and one nuclear spin coupled via the hyperfine interaction. Even for such a small spin system, the theoretical understanding is complicated by the contact with the lattice and the microwave irradiation. Both being weak, they can be treated within perturbation theory. In this work, we analyze the two most popular perturbation schemes: the Zeeman and the eigenstate-based approaches which differ in the way the hyperfine interaction is treated. For both schemes, we derive from first principles an effective Liouville equation which describes the density matrix of the spin system; we then study numerically the behavior of the nuclear polarization for several values of the hyperfine coupling. In general, we obtain that the Zeeman-based approach underestimates the value of the nuclear polarization. By performing a projection onto the diagonal part of the spin-system density matrix, we are able to understand the origin of the discrepancy, which is due to the presence of parasite leakage transitions appearing whenever the Zeeman basis is employed.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Rudolf Peierls Centre for Theoretical Physics

## Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model

### Kirill Plekhanov

^{1, 2}Ivana Vasić^{3}Alexandru Petrescu^{4}Rajbir Nirwan^{5}Guillaume Roux^{2}Walter Hofstetter^{5}Karyn Le Hur^{1}*Physical Review Letters*, American Physical Society, 2018, 120 (15), 〈10.1103/PhysRevLett.120.157201〉Recently, the frustrated XY model for spins-1/2 on the honeycomb lattice has attracted a lot of attention in relation with the possibility to realize a chiral spin liquid state. This model is relevant to the physics of some quantum magnets. Using the flexibility of ultra-cold atoms setups, we propose an alternative way to realize this model through the Mott regime of the bosonic Kane-Mele-Hubbard model. The phase diagram of this model is derived using the bosonic dynamical mean-field theory. Focussing on the Mott phase, we investigate its magnetic properties as a function of frustration. We do find an emergent chiral spin state in the intermediate frustration regime. Using exact diagonalization we study more closely the physics of the effective frustrated XY model and the properties of the chiral spin state. This gapped phase displays a chiral order, breaking time-reversal and parity symmetry, but is not topologically ordered (the Chern number is zero).

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Institute of Physics [Belgrade]
- 4. EE - Department of Electrical Engineering [Princeton]
- 5. ITP - Institut für Theoretische Physik [Frankfurt am Main]

## Energy of N two-dimensional bosons with zero-range interactions

### Betzalel Bazak

^{1}Dmitry S. Petrov^{2}*New Journal of Physics*, Institute of Physics: Open Access Journals, 2018, 20 (2), 〈10.1088/1367-2630/aaa64f〉We derive an integral equation describing $N$ two-dimensional bosons with zero-range interactions and solve it for the ground state energy $B_N$ by applying a stochastic diffusion Monte Carlo scheme for up to 26 particles. We confirm and go beyond the scaling $B_N\propto 8.567^N$ predicted by Hammer and Son [Phys. Rev. Lett. {\bf 93}, 250408 (2004)] in the large-$N$ limit.

- 1. IPNO - Institut de Physique Nucléaire d'Orsay
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Extremes of $2d$ Coulomb gas: universal intermediate deviation regime

### Bertrand Lacroix-A-Chez-Toine

^{1}Aurélien Grabsch^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Science, 2018, 〈10.06222〉In this paper, we study the extreme statistics in the complex Ginibre ensemble of $N \times N$ random matrices with complex Gaussian entries, but with no other symmetries. All the $N$ eigenvalues are complex random variables and their joint distribution can be interpreted as a $2d$ Coulomb gas with a logarithmic repulsion between any pair of particles and in presence of a confining harmonic potential $v(r) \propto r^2$. We study the statistics of the eigenvalue with the largest modulus $r_{\max}$ in the complex plane. The typical and large fluctuations of $r_{\max}$ around its mean had been studied before, and they match smoothly to the right of the mean. However, it remained a puzzle to understand why the large and typical fluctuations to the left of the mean did not match. In this paper, we show that there is indeed an intermediate fluctuation regime that interpolates smoothly between the large and the typical fluctuations to the left of the mean. Moreover, we compute explicitly this "intermediate deviation function" (IDF) and show that it is universal, i.e. independent of the confining potential $v(r)$ as long as it is spherically symmetric and increases faster than $\ln r^2$ for large $r$ with an unbounded support. If the confining potential $v(r)$ has a finite support, i.e. becomes infinite beyond a finite radius, we show via explicit computation that the corresponding IDF is different. Interestingly, in the borderline case where the confining potential grows very slowly as $v(r) \sim \ln r^2$ for $r \gg 1$ with an unbounded support, the intermediate regime disappears and there is a smooth matching between the central part and the left large deviation regime.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Fluctuations of observables for free fermions in a harmonic trap at finite temperature

### Aurélien Grabsch

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}Christophe Texier^{1}*SciPost Physics Journals*, the SciPost Foundation, 2018We study a system of 1D noninteracting spinless fermions in a confining trap at finite temperature. We first derive a useful and general relation for the fluctuations of the occupation numbers valid for arbitrary confining trap, as well as for both canonical and grand canonical ensembles. Using this relation, we obtain compact expressions, in the case of the harmonic trap, for the variance of certain observables of the form of sums of a function of the fermions' positions, $\mathcal{L}=\sum_n h(x_n)$. Such observables are also called linear statistics of the positions. As anticipated, we demonstrate explicitly that these fluctuations do depend on the ensemble in the thermodynamic limit, as opposed to averaged quantities, which are ensemble independent. We have applied our general formalism to compute the fluctuations of the number of fermions $\mathcal{N}_+$ on the positive axis at finite temperature. Our analytical results are compared to numerical simulations. We discuss the universality of the results with respect to the nature of the confinement.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## High-precision simulation of the height distribution for the KPZ equation

### Alexander K. Hartmann

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{3}Alberto Rosso^{3}Gregory Schehr^{3}*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2018, 121 (6), 〈10.1209/0295-5075/121/67004〉The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling approach, the distribution is obtained over a large range of values, down to a probability density as small as 10^{-1000} in the tails. Both short and long times are investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations. At short times the agreement with the analytical expression is spectacular. We observe that the far left and right tails, with exponents 5/2 and 3/2 respectively, are preserved until large time. We present some evidence for the predicted non-trivial crossover in the left tail from the 5/2 tail exponent to the cubic tail of Tracy-Widom, although the details of the full scaling form remains beyond reach.

- 1. University of Oldenburg
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Higher-order corrections to the effective potential close to the jamming transition in the perceptron model

### Ada Altieri

^{1, 2}*Physical Review E*, American Physical Society (APS), 2018, 97 (1), 〈10.1103/PhysRevE.97.012103〉We analyze the perceptron model performing a Plefka-like expansion of the free energy. This model falls in the same universality class as hard spheres near jamming, allowing to get exact predictions in high dimensions for more complex systems. Our method enables to define an effective potential (or TAP free energy), namely a coarse-grained functional depending on the contact forces and the effective gaps between the particles. The derivation is performed up to the third order, with a particular emphasis on the role of third order corrections to the TAP free energy. These corrections, irrelevant in a mean-field framework in the thermodynamic limit, might instead play a fundamental role when considering finite-size effects. We also study the typical behavior of the forces and we show that two kinds of corrections can occur. The first contribution arises since the system is analyzed at a finite distance from jamming, while the second one is due to finite-size corrections. In our analysis, third order contributions vanish in the jamming limit, both for the potential and the generalized forces, in agreement with the argument proposed by Wyart and coworkers invoking isostaticity. Finally, we analyze the scalings emerging close to the jamming line, which define a crossover regime connecting the control parameters of the model to an effective temperature.

- 1. Department of Physics [Roma La Sapienza]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Like-charge attraction in a one-dimensional setting: the importance of being odd

### E. Trizac

^{1}G. Tellez^{2}*European Journal of Physics*, European Physical Society, 2018From cement cohesion to DNA condensation, a proper statistical physics treatment of systems with long range forces is important for a number of applications in physics, chemistry, and biology. We compute here the effective force between fixed charged macromolecules, screened by oppositely charged mobile ions (counterions). We treat the problem in a one dimensional configuration, that allows for interesting discussion and derivation of exact results, remaining at a level of mathematical difficulty compatible with an undergraduate course. Emphasis is put on the counter-intuitive but fundamental phenomenon of like-charge attraction, that our treatment brings for the first time to the level of undergraduate teaching. The parity of the number of counterions is shown to play a prominent role, which sheds light on the binding mechanism at work when like-charge macromolecules do attract.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Departamento de Fisica

## Liquid beyond the van der Waals paradigm

### Dmitry Petrov

^{1}*Nature Physics*, Nature Publishing Group, 2018, 14 (3), pp.211 - 212. 〈10.1038/s41567-018-0052-9〉- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Localization of soft modes at the depinning transition

### Xiangyu Cao

^{1}Sebastián Bouzat^{2}Alejandro B. Kolton^{2}Alberto Rosso^{1}*Physical Review E*, American Physical Society (APS), 2018, 97 (2), 〈10.1103/PhysRevE.97.022118〉We characterize the soft modes of the dynamical matrix at the depinning transition, and compare it with the properties of the Anderson model (and long--range generalizations). The density of states at the edge of the spectrum displays a universal linear tail, different from the Lifshitz tails. The eigenvectors are instead very similar in the two matrix ensembles. We focus on the ground state (soft mode), which represents the epicenter of avalanche instabilities. We expect it to be localized in all finite dimensions, and make a clear connection between its localization length and the Larkin length of the depinning model. In the fully connected model, the weak--strong pinning transition coincides with a peculiar localization transition of the ground state.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Centro Atómico Bariloche [Argentine]

## Log-correlated random-energy models with extensive free-energy fluctuations: Pathologies caused by rare events as signatures of phase transitions

### Xiangyu Cao

^{1}Yan FyodorovPierre Le Doussal^{2}*Phys.Rev.E*, 2018, 97 (2), pp.022117. 〈10.1103/PhysRevE.97.022117〉We address systematically an apparent nonphysical behavior of the free-energy moment generating function for several instances of the logarithmically correlated models: the fractional Brownian motion with Hurst index H=0 (fBm0) (and its bridge version), a one-dimensional model appearing in decaying Burgers turbulence with log-correlated initial conditions and, finally, the two-dimensional log-correlated random-energy model (logREM) introduced in Cao et al. [Phys. Rev. Lett. 118, 090601 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.090601] based on the two-dimensional Gaussian free field with background charges and directly related to the Liouville field theory. All these models share anomalously large fluctuations of the associated free energy, with a variance proportional to the log of the system size. We argue that a seemingly nonphysical vanishing of the moment generating function for some values of parameters is related to the termination point transition (i.e., prefreezing). We study the associated universal log corrections in the frozen phase, both for logREMs and for the standard REM, filling a gap in the literature. For the above mentioned integrable instances of logREMs, we predict the nontrivial free-energy cumulants describing non-Gaussian fluctuations on the top of the Gaussian with extensive variance. Some of the predictions are tested numerically.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Matrix product algorithm for stochastic dynamics on networks applied to nonequilibrium Glauber dynamics

### Thomas Barthel

^{1, 2}Caterina De Bacco^{2, 3}Silvio Franz^{2}*Physical Review E*, American Physical Society (APS), 2018, 97 (1), 〈10.1103/PhysRevE.97.010104〉We introduce and apply a novel efficient method for the precise simulation of stochastic dynamical processes on locally tree-like graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for example, to spin-glass systems, Boolean networks, neural networks, or other technological, biological, and social networks. Building upon ideas from quantum many-body theory, the new approach is based on a matrix product approximation of the so-called edge messages -- conditional probabilities of vertex variable trajectories. Computation costs and accuracy can be tuned by controlling the matrix dimensions of the matrix product edge messages (MPEM) in truncations. In contrast to Monte Carlo simulations, the algorithm has a better error scaling and works for both, single instances as well as the thermodynamic limit. We employ it to examine prototypical non-equilibrium Glauber dynamics in the kinetic Ising model. Because of the absence of cancellation effects, observables with small expectation values can be evaluated accurately, allowing for the study of decay processes and temporal correlations.

- 1. Duke university [Durham]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Santa Fe Institute

## Matrix product state description of Halperin states

### V. Crépel

^{1}B. Estienne^{2}B.A. Bernevig^{1, 3}P. Lecheminant^{4}N. Regnault^{1}*Phys.Rev.B*, 2018, 97 (16), pp.165136. 〈10.1103/PhysRevB.97.165136〉Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact matrix product state (MPS) that was extensively studied for the systems without any spin or any other internal degrees of freedom. In that case, the correlators are built from a single electronic operator, which is primary with respect to the underlying conformal field theory. We generalize this construction to the archetype of Abelian multicomponent fractional quantum Hall wave functions, the Halperin states. These can be written as conformal blocks involving multiple electronic operators and we explicitly derive their exact MPS representation. In particular, we deal with the caveat of the full wave-function symmetry and show that any additional SU(2) symmetry is preserved by the natural MPS truncation scheme provided by the conformal dimension. We use our method to characterize the topological order of the Halperin states by extracting the topological entanglement entropy. We also evaluate their bulk correlation lengths, which are compared to plasma analogy arguments.

- 1. LPA - Laboratoire Pierre Aigrain
- 2. LPTHE - Laboratoire de Physique Théorique et Hautes Energies
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. LPTM - Laboratoire de Physique Théorique et Modélisation

## Modeling of networks and globules of charged domain walls observed in pump and pulse induced states

### Petr Karpov

^{1}Serguei Brazovskii^{2, 1, 3}*Scientific Reports*, Nature Publishing Group, 2018Experiments on optical and STM injection of carriers in layered $\mathrm{MX_2}$ materials revealed the formation of nanoscale patterns with networks and globules of domain walls. This is thought to be responsible for the metallization transition of the Mott insulator and for stabilization of a "hidden" state. In response, here we present studies of the classical charged lattice gas model emulating the superlattice of polarons ubiquitous to the material of choice $1T-\mathrm{TaS_2}$. The injection pulse was simulated by introducing a small random concentration of voids which subsequent evolution was followed by means of Monte Carlo cooling. Below the detected phase transition, the voids gradually coalesce into domain walls forming locally connected globules and then the global network leading to a mosaic fragmentation into domains with different degenerate ground states. The obtained patterns closely resemble the experimental STM visualizations. The surprising aggregation of charged voids is understood by fractionalization of their charges across the walls' lines.

- 1. MISIS - National University of Science and Technology
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. IJS - Jozef Stefan Institute [Ljubljana, Slovenia]

## Momentum correlations as signature of sonic Hawking radiation in Bose-Einstein condensates

### A. Fabbri

^{1}N. Pavloff^{2}*SciPost Phys.*, 2018, 4, pp.019. 〈10.21468/SciPostPhys.4.4.019〉We study the two-body momentum correlation signal in a quasi one dimensional Bose-Einstein condensate in the presence of a sonic horizon. We identify the relevant correlation lines in momentum space and compute the intensity of the corresponding signal. We consider a set of different experimental procedures and identify the specific issues of each measuring process. We show that some inter-channel correlations, in particular the Hawking quantum-partner one, are particularly well adapted for witnessing quantum non-separability, being resilient to the effects of temperature and/or quantum quenches.

- 1. LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Negative Differential Mobility in Interacting Particle Systems

### Amit Kumar Chatterjee

^{1}Urna Basu^{2}P. K. Mohanty^{1}*Physical Review E*, American Physical Society (APS), 2018Driven particles in presence of crowded environment, obstacles or kinetic constraints often exhibit negative differential mobility (NDM) due to their decreased dynamical activity. We propose a new mechanism for complex many-particle systems where slowing down of certain {\it non-driven} degrees of freedom by the external field can give rise to NDM. This phenomenon, resulting from inter-particle interactions, is illustrated in a pedagogical example of two interacting random walkers, one of which is biased by an external field while the same field only slows down the other keeping it unbiased. We also introduce and solve exactly the steady state of several driven diffusive systems, including a two species exclusion model, asymmetric misanthrope and zero-range processes, to show explicitly that this mechanism indeed leads to NDM.

- 1. Saha Institute of Nuclear Physics
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry

### Christophe Texier

^{1, 2}Johannes Mitscherling^{1, 3}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018, 〈10.02214〉We study the non-linear conductance $\mathcal{G}\sim\partial^2I/\partial V^2|_{V=0}$ in coherent quasi-1D weakly disordered metallic wires. The analysis is based on the calculation of two fundamental correlators (correlations of conductance's functional derivatives and correlations of injectivities), which are obtained explicitly by using diagrammatic techniques. In a coherent wire of length $L$, we obtain $\mathcal{G}\sim0.006\,E_\mathrm{Th}^{-1}$ (and $\langle\mathcal{G}\rangle=0$), where $E_\mathrm{Th}=D/L^2$ is the Thouless energy and $D$ the diffusion constant; the small dimensionless factor results from screening, i.e. cannot be obtained within a simple theory for non-interacting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal: the antisymmetric part of the non-linear conductance (at high magnetic field) being much smaller than the symmetric one, $\mathcal{G}_a\sim0.001\,(gE_\mathrm{Th})^{-1}$, where $g\gg1$ is the dimensionless (linear) conductance of the wire. Weakly coherent regimes are also studied: for $L_\varphi\ll L$, where $L_\varphi$ is the phase coherence length, we get $\mathcal{G}\sim(L_\varphi/L)^{7/2}E_\mathrm{Th}^{-1}$, and $\mathcal{G}_a\sim(L_\varphi/L)^{11/2}(gE_\mathrm{Th})^{-1}\ll\mathcal{G}$ (at high magnetic field). When thermal fluctuations are important, $L_T\ll L_\varphi\ll L$ where $L_T=\sqrt{D/T}$, we obtain $\mathcal{G}\sim(L_T/L)(L_\varphi/L)^{7/2}E_\mathrm{Th}^{-1}$ (the result is dominated by the effect of screening) and $\mathcal{G}_a\sim(L_T/L)^2(L_\varphi/L)^{7/2}(gE_\mathrm{Th})^{-1}$. All the precise dimensionless prefactors are obtained. Crossovers towards the zero magnetic field regime are also analysed.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides
- 3. Max Planck Institute for Solid State Research

## On characteristic polynomials for a generalized chiral random matrix ensemble with a source

### Yan FyodorovJacek Grela

^{1}Eugene Strahov*J.Phys.A*, 2018, 51 (13), pp.134003. 〈10.1088/1751-8121/aaae2a〉We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a random matrix taken from a L-deformed chiral Gaussian Unitary Ensemble with an external source Ω. Relation to a recently studied statistics of bi-orthogonal eigenvectors in the complex Ginibre ensemble, see Fyodorov (2017 arXiv:1710.04699), is briefly discussed as a motivation to study asymptotics of these objects in the case of external source proportional to the identity matrix. In particular, for an associated complex bulk/chiral edge scaling regime we retrieve the kernel related to Bessel/Macdonald functions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Operator Product Expansion in Liouville Field Theory and Seiberg type transitions in log-correlated Random Energy Models

### Xiangyu CaoPierre Le Doussal

^{1}Alberto Rosso^{2}Raoul Santachiara^{2}*Phys.Rev.E*, 2018, 97 (4), pp.042111. 〈10.1103/PhysRevE.97.042111〉We study transitions in log-correlated random energy models (logREMs) that are related to the violation of a Seiberg bound in Liouville field theory (LFT): the binding transition and the termination point transition (a.k.a., pre-freezing). By means of LFT-logREM mapping, replica symmetry breaking and traveling-wave equation techniques, we unify both transitions in a two-parameter diagram, which describes the free-energy large deviations of logREMs with a deterministic background log potential, or equivalently, the joint moments of the free energy and Gibbs measure in logREMs without background potential. Under the LFT-logREM mapping, the transitions correspond to the competition of discrete and continuous terms in a four-point correlation function. Our results provide a statistical interpretation of a peculiar nonlocality of the operator product expansion in LFT. The results are rederived by a traveling-wave equation calculation, which shows that the features of LFT responsible for the transitions are reproduced in a simple model of diffusion with absorption. We examine also the problem by a replica symmetry breaking analysis. It complements the previous methods and reveals a rich large deviation structure of the free energy of logREMs with a deterministic background log potential. Many results are verified in the integrable circular logREM, by a replica-Coulomb gas integral approach. The related problem of common length (overlap) distribution is also considered. We provide a traveling-wave equation derivation of the LFT predictions announced in a precedent work.

- 1. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Origin of the correlations between exit times in pedestrian flows through a bottleneck

### Alexandre Nicolas

^{1}Ioannis Touloupas^{1}*Journal of Statistical Mechanics*, 2018, 1, pp.013402. 〈http://iopscience.iop.org/article/10.1088/1742-5468/aa9dcd〉Robust statistical features have emerged from the microscopic analysis of dense pedestrian flows through a bottleneck, notably with respect to the time gaps between successive passages. We pinpoint the mechanisms at the origin of these features thanks to simple models that we develop and analyse quantitatively. We disprove the idea that anticorrelations between successive time gaps (i.e., an alternation between shorter ones and longer ones) are a hallmark of a zipper-like intercalation of pedestrian lines and show that they simply result from the possibility that pedestrians from distinct 'lines' or directions cross the bottleneck within a short time interval. A second feature concerns the bursts of escapes, i.e., egresses that come in fast succession. Despite the ubiquity of exponential distributions of burst sizes, entailed by a Poisson process, we argue that anomalous (power-law) statistics arise if the bottleneck is nearly congested, albeit only in a tiny portion of parameter space. The generality of the proposed mechanisms implies that similar statistical features should also be observed for other types of particulate flows.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Phase-space study of surface-electrode Paul traps: Integrable, chaotic, and mixed motions

### V. Roberdel

^{1}D. Leibfried^{2}D. Ullmo^{1}H. Landa^{1, 3}*Physical Review A*, American Physical Society, 2018, 97 (5), 〈10.1103/PhysRevA.97.053419〉We present a comprehensive phase-space treatment of the motion of charged particles in electrodynamic traps. Focusing on five-wire surface-electrode Paul traps, we study the details of integrable and chaotic motion of a single ion. We introduce appropriate phase-space measures and give a universal characterization of the trap effectiveness as a function of the parameters. We rigorously derive the commonly used (time-independent) pseudopotential approximation, quantify its regime of validity and analyze the mechanism of its breakdown within the time-dependent potential. The phase space approach that we develop gives a general framework for describing ion dynamics in a broad variety of surface Paul traps. To probe this framework experimentally, we propose and analyze, using numerical simulations, an experiment that can be realized with an existing four-wire trap. We predict a robust experimental signature of the existence of trapping pockets within a mixed regular and chaotic phase-space structure. Intricately rich escape dynamics suggest that surface traps give access to exploring microscopic Hamiltonian transport phenomena in phase space.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. NIST - National Institute of Standards and Technologies
- 3. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Pinning by rare defects and effective mobility for elastic interfaces in high dimensions

### Xiangyu Cao

^{1}Vincent Démery^{2, 3}Alberto Rosso^{4, 5}*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2018, 51 (23), 〈10.1088/1751-8121/aac02f〉The existence of a depinning transition for a high dimensional interface in a weakly disordered medium is controversial. Following Larkin arguments and a perturbative expansion, one expects a linear response with a renormalized mobility ${\mu}_{\text{eff}}$ . In this paper, we compare these predictions with the exact solution of a fully connected model, which displays a finite critical force $f_c$. At small disorder, we unveil an intermediary linear regime for $f_c < f < 1$ characterized by the renormalized mobility ${\mu}_{\text{eff}}$. Our results suggest that in high dimension the critical force is always finite and determined by the effect of rare impurities that is missed by the perturbative expansion. However, the perturbative expansion correctly describes an intermediate regime that should be visible at small disorder.

- 1. University of California [Berkeley]
- 2. ESPCI - UMR Gulliver
- 3. Phys-ENS - Laboratoire de Physique de l'ENS Lyon
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. KITP - Kavli Institute for Theoretical Physics

## Planar screening by charge polydisperse counterions

### M. Trulsson

^{1, 2}E. Trizac^{1}L. Samaj^{3}*Journal of Physics: Condensed Matter*, IOP Publishing, 2018, 30 (3), 〈10.1088/1361-648X/aa9a79〉We study how a neutralising cloud of counterions screens the electric field of a uniformly charged planar membrane plate, when the counterions are characterised by a distribution of charges (or valence), $n(q)$. We work out analytically the one-plate and two-plate cases, at the level of non-linear Poisson-Boltzmann theory. The (essentially asymptotic) predictions are successfully compared to numerical solutions of the full Poisson-Boltzmann theory, but also to Monte Carlo simulations. The counterions with smallest valence control the long-distance features of interactions, and may qualitatively change the results pertaining to the classic monodisperse case where all counterions have the same charge. Emphasis is put on continuous distributions $n(q)$, for which new power-laws can be evidenced, be it for the ionic density or the pressure, in the one- and two-plates situations respectively. We show that for discrete distributions, more relevant for experiments, these scaling laws persist in an intermediate but yet observable range. Furthermore, it appears that from a practical point of view, hallmarks of the continuous $n(q)$ behaviour is already featured by discrete mixtures with a relatively small number of constituents.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Lund University [Lund]
- 3. Institute of Physics

## Responses to auxin signals: an operating principle for dynamical sensitivity yet high resilience

### Silvia Grigolon

^{1}Barbara Bravi^{2}Olivier C. Martin^{1, 3}*Royal Society Open Science*, The Royal Society, 2018, 5 (1), 〈10.1098/rsos.172098〉Plants depend on the signaling of the phytohormone auxin for their development and for responding to environmental perturbations. The associated biomolecular signaling network involves a negative feedback at the level of the Aux/IAA proteins which mediate the influence of auxin (the signal) on the ARF transcription factors (the drivers of the response). To probe the role of this feedback, we consider alternative in silico signaling networks implementing different operating principles. By a comparative analysis, we find that the presence of a negative regulatory feedback loop allows the system to have a far larger sensitivity in its dynamical response to auxin. At the same time, this sensitivity does not prevent the system from being highly resilient. Given this insight, we reconsider previously published models and build a new quantitative and calibrated biomolecular model of auxin signaling.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. King‘s College London [London]
- 3. GQE-Le Moulon - Génétique Quantitative et Evolution - Le Moulon (Génétique Végétale)

## Role of City Texture in Urban Heat Islands at Nighttime

### J.M. SobstylT. Emig

^{1}M.J. QomiF.-J. UlmR.J.-M. Pellenq*Physical Review Letters*, American Physical Society, 2018, 120 (10), pp.108701. 〈10.1103/PhysRevLett.120.108701〉An urban heat island (UHI) is a climate phenomenon that results in an increased air temperature in cities when compared to their rural surroundings. In this Letter, the dependence of an UHI on urban geometry is studied. Multiyear urban-rural temperature differences and building footprints data combined with a heat radiation scaling model are used to demonstrate for more than 50 cities worldwide that city texture—measured by a building distribution function and the sky view factor—explains city-to-city variations in nocturnal UHIs. Our results show a strong correlation between nocturnal UHIs and the city texture.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Singularities of Floquet scattering and tunneling

### H. Landa

^{1, 2}*Physical Review A*, American Physical Society, 2018, 97 (4), 〈10.1103/PhysRevA.97.042705〉We study quasi-bound states and scattering with short range potentials in three dimensions, subject to an axial periodic driving. We find that poles of the scattering S-matrix can cross the real energy axis as a function of the drive amplitude, making the S-matrix nonanalytic at a singular point. For the corresponding quasi-bound states that can tunnel out of (or get captured within) a potential well, this results in a discontinuous jump in both the angular momentum and energy of emitted (absorbed) waves. We also analyze elastic and inelastic scattering of slow particles in the time dependent potential. For a drive amplitude at the singular point, there is a total absorption of incoming low energy (s-wave) particles and their conversion to high energy outgoing (mostly p-) waves. We examine the relation of such Floquet singularities, lacking in an effective time independent approximation, with well known "spectral singularities" (or "exceptional points"). These results are based on an analytic approach for obtaining eigensolutions of time-dependent periodic Hamiltonians with mixed cylindrical and spherical symmetry, and apply broadly to particles interacting via power law forces and subject to periodic fields, e.g. co-trapped ions and atoms.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IPHT - Institut de Physique Théorique - UMR CNRS 3681

## Soft modes and strain redistribution in continuous models of amorphous plasticity: the Eshelby paradigm, and beyond?

### Xiangyu Cao

^{1, 2}Alexandre Nicolas^{1}Denny Trimcev^{1, 3}Alberto Rosso^{1}*Soft Matter*, Royal Society of Chemistry, 2018, 14 (18), pp.3640 - 3651. 〈10.1039/C7SM02510F〉The deformation of disordered solids relies on swift and localised rearrangements of particles. The inspection of soft vibrational modes can help predict the locations of these rearrangements, while the strain that they actually redistribute mediates collective effects. Here, we study soft modes and strain redistribution in a two-dimensional continuous mesoscopic model based on a Ginzburg-Landau free energy for perfect solids, supplemented with a plastic disorder potential that accounts for shear softening and rearrangements. Regardless of the disorder strength, our numerical simulations show soft modes that are always sharply peaked at the softest point of the material (unlike what happens for the depinning of an elastic interface). Contrary to widespread views, the deformation halo around this peak does not always have a quadrupolar (Eshelby-like) shape. Instead, for finite and narrowly-distributed disorder, it looks like a fracture, with a strain field that concentrates along some easy directions. These findings are rationalised with analytical calculations in the case where the plastic disorder is confined to a point-like `impurity'. In this case, we unveil a continuous family of elastic propagators, which are identical for the soft modes and for the equilibrium configurations. This family interpolates between the standard quadrupolar propagator and the fracture-like one as the anisotropy of the elastic medium is increased. Therefore, we expect to see a fracture-like propagator when extended regions on the brink of failure have already softened along the shear direction and thus rendered the material anisotropic, but not failed yet. We speculate that this might be the case in carefully aged glasses just before macroscopic failure.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of California [Berkeley]
- 3. ENS Paris - École normale supérieure - Paris

## Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension

### Kanaya Malakar

^{1}V. Jemseena^{2}Anupam Kundu^{2}K. Vijay Kumar^{2}Sanjib Sabhapandit^{3}Satya N. Majumdar^{4}S. Redner^{5}Abhishek Dhar^{2}*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2018We investigate the motion of a run-and-tumble particle (RTP) in one dimension. We find the exact probability distribution of the particle with and without diffusion on the infinite line, as well as in a finite interval. In the infinite domain, this probability distribution approaches a Gaussian form in the long-time limit, as in the case of a regular Brownian particle. At intermediate times, this distribution exhibits unexpected multi-modal forms. In a finite domain, the probability distribution reaches a steady state form with peaks at the boundaries, in contrast to a Brownian particle. We also study the relaxation to the steady state analytically. Finally we compute the survival probability of the RTP in a semi-infinite domain. In the finite interval, we compute the exit probability and the associated exit times. We provide numerical verifications of our analytical results.

- 1. Presidency University
- 2. International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
- 3. Raman Research Institute
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. Santa Fe Institute

## Strong-coupling theory of counterions between symmetrically charged walls: from crystal to fluid phases

### L. Samaj

^{1}M. Trulsson^{2}E. Trizac^{3}*Soft Matter*, Royal Society of Chemistry, 2018We study thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance $d$. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle deviations is made around the bilayer positions, with a free lattice parameter determined from a variational approach. For each of the two walls, the harmonic expansion implies an effective one-body potential at the root of all observables of interest in our Wigner Strong-Coupling expansion. Analytical results for the particle density profile and the pressure are in good agreement with numerical Monte Carlo data, for small as well as intermediate values of $d$ comparable with the Wigner lattice spacing. While the strong-coupling theory is extended to the fluid regime by using the concept of a correlation hole, the Wigner calculations appear trustworthy for all electrostatic couplings investigated. Our results significantly extend the range of accuracy of analytical equations of state for strongly interacting charged planar interfaces.

- 1. Institute of Physics
- 2. Lund University [Lund]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Superfluidity of identical fermions in an optical lattice: Atoms and polar molecules

### A. K. Fedorov

^{1}V. I. Yudson^{2}G. V. Shlyapnikov^{3, 4, 1}*AIP Conference Proceedings*, American Institute of Physics, 2018, 〈10.1063/1.5025460〉In this work, we discuss the emergence of $p$-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices, for short-range interacting atoms, the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the $p$-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create atomic $p$-wave superfluids with sizable transition temperatures. The situation is drastically different for fermionic polar molecules. Being dressed with a microwave field, they acquire a dipole-dipole attractive tail in the interaction potential. Then, due to a long-range character of the dipole-dipole interaction, the effect of the suppression of the scattering amplitude in 2D lattices is absent. This leads to the emergence of a stable topological $p_x+ip_y$ superfluid of identical microwave-dressed polar molecules.

- 1. Russian Quantum Center
- 2. Institute of Spectroscopy
- 3. Wuhan Institute of Physics and Mathematics
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Surface temperatures in New York City: Geospatial data enables the accurate prediction of radiative heat transfer

### Masoud Ghandehari

^{1}Thorsten Emig^{2, 3}Milad Aghamohamadnia^{1}*Scientific Reports*, Nature Publishing Group, 2018Three decades into the research seeking to derive the urban energy budget, the dynamics of the thermal exchange between the densely built infrastructure and the environment are still not well understood. We present a novel hybrid experimental-numerical approach for the analysis of the radiative heat transfer in New York City. The aim of this work is to contribute to the calculation of the urban energy budget, in particular the stored energy. Improved understanding of urban thermodynamics incorporating the interaction of the various bodies will have implications on energy conservation at the building scale, as well as human health and comfort at the urban scale. The platform presented is based on longwave hyperspectral imaging of nearly 100 blocks of Manhattan, and a geospatial radiosity model that describes the collective radiative heat exchange between multiple buildings. The close comparison of temperature values derived from measurements and the computed surface temperatures (including streets and roads) implies that this geospatial, thermodynamic numerical model applied to urban structures, is promising for accurate and high resolution analysis of urban surface temperatures.

- 1. NYU Tandon School of Engineering
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. MSE2 - Multiscale Materials Science for Energy and Environment

## The impact of the injection protocol on an impurity’s stationary state

### Oleksandr Gamayun

^{1, 2}Oleg Lychkovskiy^{3, 4, 5}Evgeni Burovski^{6, 7}Matthew Malcomson^{8}Vadim V. Cheianov^{1}Mikhail B. Zvonarev^{9}*Physical Review Letters*, American Physical Society, 2018We examine stationary state properties of an impurity particle injected into a one-dimensional quantum gas. We show that the value of the impurity's end velocity lies between zero and the speed of sound in the gas, and is determined by the injection protocol. This way, the impurity's constant motion is a dynamically emergent phenomenon whose description goes beyond accounting for the kinematic constraints of Landau approach to superfluidity. We provide exact analytic results in the thermodynamic limit, and perform finite-size numerical simulations to demonstrate that the predicted phenomena are within the reach of the existing ultracold gases experiments.

- 1. Universiteit Leiden [Leiden]
- 2. Bogolyubov Institute for Theoretical Physics
- 3. Skoltech - Skolkovo Institute of Science and Technology [Moscow]
- 4. Steklov Mathematical Institute of Russian Academy of Sciences
- 5. Russian Quantum Center
- 6. National Research University Higher School of Economics [Moscow]
- 7. Science Center in Chernogolovka
- 8. Lancaster University
- 9. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Topological Zak Phase in Strongly-Coupled LC Circuits

### Tal Goren

^{1}Kirill Plekhanov^{1, 2}Félicien Appas^{1}Karyn Le Hur^{1}*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2018We show the emergence of topological Bogoliubov bosonic excitations in the relatively strong coupling limit of an LC (inductance-capacitance) one-dimensional quantum circuit. This dimerized chain model reveals a ${\cal Z}_2$ local symmetry as a result of the counter-rotating wave (pairing) terms. The topology is protected by the sub-lattice symmetry, represented by an anti-unitary transformation. We present a methos to measure the winding of the topological Zak phase across the Brillouin zone by a reflection measurement of (microwave) light. Our method probes bulk quantities and can be implemented even in small systems. We study the robustness of edge modes towards disorder.

- 1. CPHT - Centre de Physique Théorique [Palaiseau]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Towards Quantum Simulation with Circular Rydberg Atoms

### Thanh Long Nguyen

^{1}Jean-Michel Raimond^{1}Clément Sayrin^{1}Rodrigo Cortinas^{1}Tigrane Cantat-Moltrecht^{1}Fédéric Assemat^{1}Igor Dotsenko^{1}Sébastien Gleyzes^{1}Serge Haroche^{1}Guillaume Roux^{2}Thierry Jolicoeur^{2}Michel Brune^{1}*Physical Review X*, American Physical Society, 2018, 8 (1), 〈10.1103/PhysRevX.8.011032〉The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic approaches to many-body systems are limited and the huge size of their Hilbert space makes numerical simulations on classical computers intractable. A quantum simulator avoids these limitations by transcribing the system of interest into another, with the same dynamics but with interaction parameters under control and with experimental access to all relevant observables. Quantum simulation of spin systems is being explored with trapped ions, neutral atoms and superconducting devices. We propose here a new paradigm for quantum simulation of spin-1/2 arrays providing unprecedented flexibility and allowing one to explore domains beyond the reach of other platforms. It is based on laser-trapped circular Rydberg atoms. Their long intrinsic lifetimes combined with the inhibition of their microwave spontaneous emission and their low sensitivity to collisions and photoionization make trapping lifetimes in the minute range realistic with state-of-the-art techniques. Ultra-cold defect-free circular atom chains can be prepared by a variant of the evaporative cooling method. This method also leads to the individual detection of arbitrary spin observables. The proposed simulator realizes an XXZ spin-1/2 Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kHz. All the model parameters can be tuned at will, making a large range of simulations accessible. The system evolution can be followed over times in the range of seconds, long enough to be relevant for ground-state adiabatic preparation and for the study of thermalization, disorder or Floquet time crystals. This platform presents unrivaled features for quantum simulation.

- 1. LKB [Collège de France] - Laboratoire Kastler Brossel
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques