# 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 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 – 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

## 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. 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 – 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 – 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

## 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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 – 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. QomiF.-J. UlmR.J.-M. Pellenq*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

## 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 – 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 – 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 – 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 – 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

## 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