Publications 2020
Publications de l'année 2020 :

Actin modulates shape and mechanics of tubular membranes – Archive ouverte HAL
A. Allard ^{1} M. Bouzid ^{2} T. Betz ^{3} C. SimonM. AbouGhaliJ. Lemiere ^{4} F. Valentino ^{5} J. Manzi ^{4} F. BrochardWyart ^{6} K. Guevorkian ^{6} J. Plastino ^{6} M. Lenz ^{2} C. Campillo ^{7} C. Sykes ^{6}
A. Allard, M. Bouzid, T. Betz, C. Simon, M. AbouGhali, et al.. Actin modulates shape and mechanics of tubular membranes. Science Advances , American Association for the Advancement of Science (AAAS), 2020, 6 (17), pp.eaaz3050. ⟨10.1126/sciadv.aaz3050⟩. ⟨hal02565199⟩
 1. LNE  Laboratoire National de Métrologie et d'Essais [Trappes]
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 3. Atominstitut
 4. PCC  PhysicoChimieCurie
 5. DTU Space  National Space Institute [Lyngby]
 6. PCC  PhysicoChimieCurie
 7. inconnu

Archive ouverte HAL – Actin modulates shape and mechanics of tubular membranes
A. Allard ^{1} M. Bouzid ^{2} T. Betz ^{3} C. SimonM. AbouGhaliJ. Lemiere ^{4} F. Valentino ^{5} J. Manzi ^{4} F. BrochardWyart ^{6} K. Guevorkian ^{6} J. Plastino ^{6} M. Lenz ^{2} C. Campillo ^{7} C. Sykes ^{6}
A. Allard, M. Bouzid, T. Betz, C. Simon, M. AbouGhali, et al.. Actin modulates shape and mechanics of tubular membranes. Science Advances , American Association for the Advancement of Science (AAAS), 2020, 6 (17), pp.eaaz3050. ⟨10.1126/sciadv.aaz3050⟩. ⟨hal02565199⟩
 1. LNE  Laboratoire National de Métrologie et d'Essais [Trappes]
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 3. Atominstitut
 4. PCC  PhysicoChimieCurie
 5. DTU Space  National Space Institute [Lyngby]
 6. PCC  PhysicoChimieCurie
 7. inconnu

Archive ouverte HAL – Asymptotic behavior of the length of the longest increasing subsequences of random walks
J. Ricardo G. Mendonça ^{1} Hendrik Schawe ^{2} Alexander K. Hartmann ^{3} Alexander Hartmann
J. Ricardo G. Mendonça, Hendrik Schawe, Alexander K. Hartmann, Alexander Hartmann. Asymptotic behavior of the length of the longest increasing subsequences of random walks. Physical Review E , American Physical Society (APS), 2020, 101 (3), ⟨10.1103/PhysRevE.101.032102⟩. ⟨hal02512208⟩
We numerically estimate the leading asymptotic behavior of the length $L_{n}$ of the longest increasing subsequence of random walks with step increments following Student's $t$distribution with parameter in the range $1/2 \leq \nu \leq 5$. We find that the expected value $\mathbb{E}(L_{n}) \sim n^{\theta}\ln{n}$ with $\theta$ decreasing from $\theta(\nu=1/2) \approx 0.70$ to $\theta(\nu \geq 5/2) \approx 0.50$. For random walks with distribution of step increments of finite variance ($\nu > 2$), this confirms previous observation of $\mathbb{E}(L_{n}) \sim \sqrt{n}\ln{n}$ to leading order. We note that this asymptotic behavior (including the subleading term) resembles that of the largest part of random integer partitions under the uniform measure and that, curiously, both random variables seem to follow Gumbel statistics. We also provide more refined estimates for the asymptotic behavior of $\mathbb{E}(L_{n})$ for random walks with step increments of finite variance.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. University of Oldenburg
 3. Institut für Physik

Archive ouverte HAL – Collective excitations of a onedimensional quantum droplet
Marek TylutkiGrigori E. AstrakharchikBoris A. Malomed ^{1} Dmitry S. Petrov ^{2} Grigori Astrakharchik ^{3} Boris Malomed ^{4} Dmitry Petrov
Marek Tylutki, Grigori E. Astrakharchik, Boris A. Malomed, Dmitry S. Petrov, Grigori Astrakharchik, et al.. Collective excitations of a onedimensional quantum droplet. Physical Review A, American Physical Society 2020, 101 (5), ⟨10.1103/PhysRevA.101.051601⟩. ⟨hal02881226⟩
We calculate the excitation spectrum of a onedimensional selfbound quantum droplet in a twocomponent bosonic mixture described by the GrossPitaevskii equation (GPE) with cubic and quadratic nonlinearities. The cubic term originates from the meanfield energy of the mixture proportional to the effective coupling constant $\delta g$, whereas the quadratic nonlinearity corresponds to the attractive beyondmeanfield contribution. The droplet properties are governed by a control parameter $\gamma\propto \delta g N^{2/3}$, where $N$ is the particle number. For large $\gamma>0$ the droplet features the flattop shape with the discrete part of its spectrum consisting of planewave Bogoliubov phonons propagating through the flatdensity bulk and reflected by edges of the droplet. With decreasing $\gamma$ these modes cross into the continuum, sequentially crossing the particleemission threshold at specific critical values. A notable exception is the breathing mode which we find to be always bound. The balance point $\gamma = 0$ provides implementation of a system governed by the GPE with an unusual quadratic nonlinearity. This case is characterized by the ratio of the breathingmode frequency to the particleemission threshold equal to 0.8904. As $\gamma$ tends to $\infty$ this ratio tends to 1 and the droplet transforms into the soliton solution of the integrable cubic GPE.
 1. Tel Aviv University [Tel Aviv]
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 3. UPC  Universitat Politècnica de Catalunya [BarcelonaTech]
 4. Department of Interdisciplinary Studies

Archive ouverte HAL – Comment on “Effective Confining Potential of Quantum States in Disordered Media”
Alain Comtet ^{1} Christophe Texier ^{1}
Alain Comtet, Christophe Texier. Comment on “Effective Confining Potential of Quantum States in Disordered Media”. Physical Review Letters, American Physical Society, 2020, 124 (21), ⟨10.1103/PhysRevLett.124.219701⟩. ⟨hal02881221⟩
We provide some analytical tests of the density of states estimation from the "localization landscape" approach of Ref. [Phys. Rev. Lett. 116, 056602 (2016)]. We consider two different solvable models for which we obtain the distribution of the landscape function and argue that the precise spectral singularities are not reproduced by the estimation of the landscape approach.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Critical energy landscape of linear soft spheres
Silvio Franz ^{1} Antonio Sclocchi ^{1} Pierfrancesco Urbani ^{2}
Silvio Franz, Antonio Sclocchi, Pierfrancesco Urbani. Critical energy landscape of linear soft spheres. SciPost Physics, SciPost Foundation, 2020. ⟨hal02908534⟩
We show that soft spheres interacting with a linear ramp potential when overcompressed beyond the jamming point fall in an amorphous solid phase which is critical, mechanically marginally stable and share many features with the jamming point itself. In the whole phase, the relevant local minima of the potential energy landscape display an isostatic contact network of perfectly touching spheres whose statistics is controlled by an infinite lengthscale. Excitations around such energy minima are nonlinear, system spanning, and characterized by a set of nontrivial critical exponents. We perform numerical simulations to measure their values and show that, while they coincide, within numerical precision, with the critical exponents appearing at jamming, the nature of the corresponding excitations is richer. Therefore, linear soft spheres appear as a novel class of finite dimensional systems that selforganize into new, critical, marginally stable, states.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. IPHT  Institut de Physique Théorique  UMR CNRS 3681

Archive ouverte HAL – Current fluctuations in noninteracting runandtumble particles in one dimension
Tirthankar Banerjee ^{1} Satya N. Majumdar ^{1} Alberto Rosso ^{1} Satya Majumdar ^{1} Gregory Schehr ^{1}
Tirthankar Banerjee, Satya N. Majumdar, Alberto Rosso, Satya Majumdar, Gregory Schehr. Current fluctuations in noninteracting runandtumble particles in one dimension. Physical Review E , American Physical Society (APS), 2020, 101 (5), ⟨10.1103/PhysRevE.101.052101⟩. ⟨hal02565189⟩
We present a general framework to study the distribution of the flux through the origin up to time $t$, in a noninteracting onedimensional system of particles with a step initial condition with a fixed density $\rho$ of particles to the left of the origin. We focus principally on two cases: (i) when the particles undergo diffusive dynamics (passive case) and (ii) runandtumble dynamics for each particle (active case). In analogy with disordered systems, we consider the flux distribution both for the annealed and the quenched initial conditions, for the passive and active particles. In the annealed case, we show that, for arbitrary particle dynamics, the flux distribution is a Poissonian with a mean $\mu(t)$ that we compute exactly in terms of the Green's function of the single particle dynamics. For the quenched case, we show that, for the runandtumble dynamics, the quenched flux distribution takes an anomalous large deviation form at large times $P_{\rm qu}(Q,t) \sim \exp\left[\rho\, v_0\, \gamma \, t^2 \psi_{\rm RTP}\left(\frac{Q}{\rho v_0\,t} \right) \right]$, where $\gamma$ is the rate of tumbling and $v_0$ is the ballistic speed between two successive tumblings. In this paper, we compute the rate function $\psi_{\rm RTP}(q)$ and show that it is nontrivial. Our method also gives access to the probability of the rare event that, at time $t$, there is no particle to the right of the origin. For diffusive and runandtumble dynamics, we find that this probability decays with time as a stretched exponential, $\sim \exp(c\, \sqrt{t})$ where the constant $c$ can be computed exactly. We verify our results for these large deviations by using an importance sampling MonteCarlo method.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Departing from thermality of analogue Hawking radiation in a BoseEinstein condensate
M. Isoard ^{1} N. Pavloff ^{1}
M. Isoard, N. Pavloff. Departing from thermality of analogue Hawking radiation in a BoseEinstein condensate. Phys.Rev.Lett., 2020, 124 (6), pp.060401. ⟨10.1103/PhysRevLett.124.060401⟩. ⟨hal02317273⟩
We study the quantum fluctuations in a onedimensional BoseEinstein condensate realizing an analogous acoustic black hole. The taking into account of evanescent channels and of zero modes makes it possible to accurately reproduce recent experimental measurements of the density correlation function. We discuss the determination of Hawking temperature and show that in our model the analogous radiation presents some significant departure from thermality.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Dispersionless evolution of inviscid nonlinear pulses
M. Isoard ^{1} N. Pavloff ^{1} A. M. Kamchatnov ^{2}
M. Isoard, N. Pavloff, A. M. Kamchatnov. Dispersionless evolution of inviscid nonlinear pulses. EPL  Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2020. ⟨hal02565206⟩
We consider the onedimensional dynamics of nonlinear nondispersive waves. The problem can be mapped onto a linear one by means of the hodograph transform. We propose an approximate scheme for solving the corresponding EulerPoisson equation which is valid for any kind of nonlinearity. The approach is exact for monoatomic classical gas and agrees very well with exact results and numerical simulations for other systems. We also provide a simple and accurate determination of the wave breaking time for typical initial conditions.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. Institute of Spectroscopy

Archive ouverte HAL – Distribution of the time between maximum and minimum of random walks
Francesco Mori ^{1} Satya N. Majumdar ^{1} Satya Majumdar ^{1} Gregory Schehr ^{1}
Francesco Mori, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Distribution of the time between maximum and minimum of random walks. Physical Review E , American Physical Society (APS), 2020, 101 (5), ⟨10.1103/PhysRevE.101.052111⟩. ⟨hal02881215⟩
We consider a onedimensional Brownian motion of fixed duration $T$. Using a pathintegral technique, we compute exactly the probability distribution of the difference $\tau=t_{\min}t_{\max}$ between the time $t_{\min}$ of the global minimum and the time $t_{\max}$ of the global maximum. We extend this result to a Brownian bridge, i.e. a periodic Brownian motion of period $T$. In both cases, we compute analytically the first few moments of $\tau$, as well as the covariance of $t_{\max}$ and $t_{\min}$, showing that these times are anticorrelated. We demonstrate that the distribution of $\tau$ for Brownian motion is valid for discretetime random walks with $n$ steps and with a finite jump variance, in the limit $n\to \infty$. In the case of L\'evy flights, which have a divergent jump variance, we numerically verify that the distribution of $\tau$ differs from the Brownian case. For random walks with continuous and symmetric jumps we numerically verify that the probability of the event "$\tau = n$" is exactly $1/(2n)$ for any finite $n$, independently of the jump distribution. Our results can be also applied to describe the distance between the maximal and minimal height of $(1+1)$dimensional stationarystate KardarParisiZhang interfaces growing over a substrate of finite size $L$. Our findings are confirmed by numerical simulations. Some of these results have been announced in a recent Letter [Phys. Rev. Lett. 123, 200201 (2019)].
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Dynamical Heart Beat Correlations during Running
Matti MolkkariGiorgio Angelotti ^{1} Thorsten Emig ^{1} Esa Rasanen ^{1}
Matti Molkkari, Giorgio Angelotti, Thorsten Emig, Esa Rasanen. Dynamical Heart Beat Correlations during Running. Sci.Rep., 2020, 10, pp.13627. ⟨10.1038/s41598020703587⟩. ⟨hal02423731⟩
Fluctuations of the human heart beat constitute a complex system that has been studied mostly under resting conditions using conventional time series analysis methods. During physical exercise, the variability of the fluctuations is reduced, and the time series of beattobeat RR intervals (RRIs) become highly nonstationary. Here we develop a dynamical approach to analyze the time evolution of RRI correlations in running across various training and racing events under realworld conditions. In particular, we introduce dynamical detrended fluctuation analysis and dynamical partial autocorrelation functions, which are able to detect realtime changes in the scaling and correlations of the RRIs as functions of the scale and the lag. We relate these changes to the exercise intensity quantified by the heart rate (HR). Beyond subjectspecific HR thresholds the RRIs show multiscale anticorrelations with both universal and individual scaledependent structure that is potentially affected by the stride frequency. These preliminary results are encouraging for future applications of the dynamical statistical analysis in exercise physiology and cardiology, and the presented methodology is also applicable across various disciplines.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Extreme value statistics of correlated random variables: a pedagogical review
Satya N. Majumdar ^{1} Arnab PalGregory Schehr ^{1}
Satya N. Majumdar, Arnab Pal, Gregory Schehr. Extreme value statistics of correlated random variables: a pedagogical review. Physics Reports, Elsevier, 2020, ⟨10.10667⟩. ⟨hal02512248⟩
Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any timeseries and has applications in climate, finance, sports, all the way to physics of disordered systems where one is interested in the statistics of the ground state energy. While the EVS of `uncorrelated' variables are well understood, little is known for strongly correlated random variables. Only recently this subject has gained much importance both in statistical physics and in probability theory. In this review, we will first recall the classical EVS for uncorrelated variables and discuss the three universality classes of extreme value limiting distribution, known as the Gumbel, Fr\'echet and Weibull distribution. We then show that, for weakly correlated random variables with a finite correlation length/time, the limiting extreme value distribution can still be inferred from that of the uncorrelated variables using a renormalisation grouplike argument. Finally, we consider the most interesting examples of strongly correlated variables for which there are very few exact results for the EVS. We discuss few examples of such strongly correlated systems (such as the Brownian motion and the eigenvalues of a random matrix) where some analytical progress can be made. We also discuss other observables related to extremes, such as the density of nearextreme events, time at which an extreme value occurs, order and record statistics, etc.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Fewbody bound states of twodimensional bosons
G. Guijarro ^{1} G. E. Astrakharchik ^{1} J. Boronat ^{1} B. BazakD. S. Petrov ^{2}
G. Guijarro, G. E. Astrakharchik, J. Boronat, B. Bazak, D. S. Petrov. Fewbody bound states of twodimensional bosons. Physical Review A, American Physical Society 2020, ⟨10.1103/PhysRevA.101.041602⟩. ⟨hal02537195⟩
We study clusters of the type A$_N$B$_M$ with $N\leq M\leq 3$ in a twodimensional mixture of A and B bosons, with attractive AB and equally repulsive AA and BB interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths $a_{AB}$ and $a_{AA}=a_{BB}$, for sufficiently large attractiontorepulsion ratios $a_{AB}/a_{BB}$. When $a_{AB}/a_{BB}$ decreases below $\approx 10$, the dimerdimer interaction changes from attractive to repulsive and the populationbalanced AABB and AAABBB clusters break into AB dimers. Calculating the AAABBB hexamer energy just below this threshold, we find an effective threedimer repulsion which may have important implications for the manybody problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The populationimbalanced ABB trimer, ABBB tetramer, and AABBB pentamer remain bound beyond the dimerdimer threshold. In the dipolar model, they break up at $a_{AB}\approx 2 a_{BB}$ where the atomdimer interaction switches to repulsion.
 1. UPC  Universitat Politècnica de Catalunya [Barcelona]
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Finitetime adiabatic processes: Derivation and speed limit
Carlos Plata ^{1} David GuéryOdelin ^{2} Emmanuel Trizac ^{3} Antonio Prados ^{4}
Carlos Plata, David GuéryOdelin, Emmanuel Trizac, Antonio Prados. Finitetime adiabatic processes: Derivation and speed limit. Physical Review E , American Physical Society (APS), 2020, 101 (3), ⟨10.1103/PhysRevE.101.032129⟩. ⟨hal02535447⟩
Obtaining adiabatic processes that connect equilibrium states in a given time represents a challenge for mesoscopic systems. In this paper, we explicitly show how to build these finitetime adiabatic processes for an overdamped Brownian particle in an arbitrary potential, a system that is relevant both at the conceptual and the practical level. This is achieved by jointly engineering the time evolutions of the binding potential and the fluid temperature. Moreover, we prove that the second principle imposes a speed limit for such adiabatic transformations: there appears a minimum time to connect the initial and final states. This minimum time can be explicitly calculated for a general compression/decompression situation.
 1. Padova University
 2. Atomes Froids (LCAR)
 3. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 4. Universidad de Sevilla

Archive ouverte HAL – Locally quasistationary states in noninteracting spin chains
Maurizio Fagotti ^{1}
Maurizio Fagotti. Locally quasistationary states in noninteracting spin chains. SciPost Phys., 2020, 8, pp.048. ⟨10.21468/SciPostPhys.8.3.048⟩. ⟨hal02423699⟩
Locally quasistationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By solving the dynamics in inhomogeneous noninteracting spin chains, we identify the set of LQSSs as a subspace that is invariant under time evolution, and we explicitly construct the latter in a generalised XY model. As a byproduct, we exhibit an exact generalised hydrodynamic theory (including "quantum corrections").
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Mapping and Modeling the Nanomechanics of Bare and ProteinCoated Lipid Nanotubes
Guillaume Lamour ^{1} Antoine Allard ^{1, 2} Juan Pelta ^{1} Sid Labdi ^{1} Martin Lenz ^{3} Clément Campillo ^{1}
Guillaume Lamour, Antoine Allard, Juan Pelta, Sid Labdi, Martin Lenz, et al.. Mapping and Modeling the Nanomechanics of Bare and ProteinCoated Lipid Nanotubes. Physical Review X, American Physical Society, 2020, 10 (1), pp.011031. ⟨10.1103/PhysRevX.10.011031⟩. ⟨hal02512272⟩
Membrane nanotubes are continuously assembled and disassembled by the cell to generate and dispatch transport vesicles, for instance, in endocytosis. While these processes crucially involve the illunderstood local mechanics of the nanotube, existing micromanipulation assays only give access to its global mechanical properties. Here we develop a new platform to study this local mechanics using atomic force microscopy (AFM). On a single coverslip we quickly generate millions of substratebound nanotubes, out of which dozens can be imaged by AFM in a single experiment. A full theoretical description of the AFM tipmembrane interaction allows us to accurately relate AFM measurements of the nanotube heights, widths, and rigidities to the membrane bending rigidity and tension, thus demonstrating our assay as an accurate probe of nanotube mechanics. We reveal a universal relationship between nanotube height and rigidity, which is unaffected by the specific conditions of attachment to the substrate. Moreover, we show that the parabolic shape of forcedisplacement curves results from thermal fluctuations of the membrane that collides intermittently with the AFM tip. We also show that membrane nanotubes can exhibit high resilience against extreme lateral compression. Finally, we mimic in vivo actin polymerization on nanotubes and use AFM to assess the induced changes in nanotube physical properties. Our assay may help unravel the local mechanics of membraneprotein interactions, including membrane remodeling in nanotube scission and vesicle formation.
 1. LAMBE  UMR 8587  Laboratoire Analyse, Modélisation et Matériaux pour la Biologie et l'Environnement
 2. PCC  PhysicoChimieCurie
 3. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Multicomponent colloidal gels: interplay between structure and mechanical properties
Claudia FerreiroCordovaMehdi Bouzid ^{1} Emanuela del GadoGiuseppe Foffi ^{2} Claudia FerreiroCórdova
Claudia FerreiroCordova, Mehdi Bouzid, Emanuela del Gado, Giuseppe Foffi, Claudia FerreiroCórdova. Multicomponent colloidal gels: interplay between structure and mechanical properties. Soft Matter, Royal Society of Chemistry, 2020, 16 (18), pp.44144421. ⟨10.1039/C9SM02410G⟩. ⟨hal02881157⟩
We present a detailed numerical study of multicomponent colloidal gels interacting sterically and obtained by arrested phase separation. Under deformation, we found that the interplay between the different intertwined networks is key. Increasing the number of component leads to softer solids that can accomodate progressively larger strain before yielding. The simulations highlight how this is the direct consequence of the purely repulsive interactions between the different components, which end up enhancing the linear response of the material. Our work {provides new insight into mechanisms at play for controlling the material properties and open the road to new design principles for} soft composite solids
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. LPS  Laboratoire de Physique des Solides

Archive ouverte HAL – Noninteracting trapped Fermions in doublewell potentials: inverted parabola kernel
Naftali R. Smith ^{1} David S. Dean ^{2} Pierre Le Doussal ^{3} Satya N. Majumdar ^{1} Grégory Schehr ^{1}
Naftali R. Smith, David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr. Noninteracting trapped Fermions in doublewell potentials: inverted parabola kernel. Phys.Rev.A, 2020, 101 (5), pp.053602. ⟨10.1103/PhysRevA.101.053602⟩. ⟨hal02484003⟩
We study a system of N noninteracting spinless fermions in a confining doublewell potential in one dimension. We show that when the Fermi energy is close to the value of the potential at its local maximum, physical properties, such as the average density and the fermion position correlation functions, display a universal behavior that depends only on the local properties of the potential near its maximum. This behavior describes the merging of two Fermi gases, which are disjoint at sufficiently low Fermi energies. We describe this behavior in terms of a correlation kernel that we compute analytically and we call it the inverted parabola kernel. As an application, we calculate the mean and variance of the number of particles in an interval of size 2L centered around the position of the local maximum, for sufficiently small L. We discuss the possibility of observing our results in experiments, as well as extensions to nonzero temperature and to higher space dimensions.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. LOMA  Laboratoire Ondes et Matière d'Aquitaine
 3. LPTENS  Laboratoire de Physique Théorique de l'ENS

Archive ouverte HAL – Numerical solution of the dynamical mean field theory of infinitedimensional equilibrium liquids
Alessandro Manacorda ^{1} Gregory Schehr ^{2} Francesco Zamponi ^{1}
Alessandro Manacorda, Gregory Schehr, Francesco Zamponi. Numerical solution of the dynamical mean field theory of infinitedimensional equilibrium liquids. Journal of Chemical Physics, American Institute of Physics, 2020, 152 (16), pp.164506. ⟨10.1063/5.0007036⟩. ⟨hal02554137⟩
 1. Systèmes Désordonnés et Applications
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States
John MartinStefan WeigertOlivier Giraud ^{1}
John Martin, Stefan Weigert, Olivier Giraud. Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States. Quantum, Verein, 2020. ⟨hal02881098⟩
Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closedform expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j=5. The closedform expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Optimizing Brownian escape rates by potential shaping
Marie Chupeau ^{1} Jannes GladrowAlexei Chepelianskii ^{2} Ulrich F. KeyserEmmanuel Trizac ^{1} Ulrich Keyser
Marie Chupeau, Jannes Gladrow, Alexei Chepelianskii, Ulrich F. Keyser, Emmanuel Trizac, et al.. Optimizing Brownian escape rates by potential shaping. Proceedings of the National Academy of Sciences of the United States of America , National Academy of Sciences, 2020, 117 (3), pp.13831388. ⟨10.1073/pnas.1910677116⟩. ⟨hal02512216⟩
Brownian escape is key to a wealth of physicochemical processes, including polymer folding, and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with increasing barrier height. Here, we show experimentally that higher, finetuned barrier profiles result in significantly enhanced escape rates in breach of the intuition relying on the above scaling law, and address in theory the corresponding conditions for maximum speedup. Importantly, our barriers end on the same energy on which they start. For overdamped dynamics, the achievable boost of escape rates is, in principle, unbounded so that the barrier optimization has to be regularized. We derive optimal profiles under two different regularizations, and uncover the efficiency of Nshaped barriers. We then demonstrate the viability of such a potential in automated microfluidic Brownian dynamics experiments using holographic optical tweezers and achieve a doubling of escape rates compared to unhindered Brownian motion. Finally, we show that this escape rate boost extends into the lowfriction inertial regime.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. LPCT  Laboratoire de PhysicoChimie Théorique

Archive ouverte HAL – Reversal of contractility as a signature of selforganization in cytoskeletal bundles
Martin Lenz ^{1}
Martin Lenz. Reversal of contractility as a signature of selforganization in cytoskeletal bundles. eLife, eLife Sciences Publication, 2020, 9, ⟨10.7554/eLife.51751⟩. ⟨hal02518848⟩
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Scalable quantum computing with qudits on a graph
E. O. Kiktenko ^{1} A. S. NikolaevaPeng XuG. V. Shlyapnikov ^{2} A. K. Fedorov ^{3}
E. O. Kiktenko, A. S. Nikolaeva, Peng Xu, G. V. Shlyapnikov, A. K. Fedorov. Scalable quantum computing with qudits on a graph. Physical Review A, American Physical Society 2020, 101 (2), ⟨10.1103/PhysRevA.101.022304⟩. ⟨hal02512218⟩
We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality of qudits and their topology of connections for a scalable multiqudit processor, where higher qudit levels are used for substituting ancillas. The suggested model is of importance for the realization of quantum algorithms and as a method of quantum error correction codes for singlequbit operations.
 1. IPE  Schmidt United Institute of Physics of the Earth [Moscow]
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 3. Russian Quantum Center

Archive ouverte HAL – State transition graph of the Preisach model and the role of returnpoint memory
M. Mert Terzi ^{1} Muhittin Mungan
M. Mert Terzi, Muhittin Mungan. State transition graph of the Preisach model and the role of returnpoint memory. Physical Review E, 2020, 102 (1), ⟨10.1103/PhysRevE.102.012122⟩. ⟨hal02908545⟩
The Preisach model has been useful as a nullmodel for understanding memory formation in periodically driven disordered systems. In amorphous solids for example, the athermal response to shear is due to localized plastic events (soft spots). As shown recently by one of us, the plastic response to applied shear can be rigorously described in terms of a directed network whose transitions correspond to one or more soft spots changing states. The topology of this graph depends on the interactions between softspots and when such interactions are negligible, the resulting description becomes that of the Preisach model. A first step in linking transition graph topology with the underlying softspot interactions is therefore to determine the structure of such graphs in the absence of interactions. Here we perform a detailed analysis of the transition graph of the Preisach model. We highlight the important role played by return point memory in organizing the graph into a hierarchy of loops and subloops. Our analysis reveals that the topology of a large portion of this graph is actually not governed by the values of the switching fields that describe the individual hysteretic behavior of the individual elements, but by a coarser parameter, a permutation $\rho$ which prescribes the sequence in which the individual hysteretic elements change their states as the main hysteresis loop is traversed. This in turn allows us to derive combinatorial properties, such as the number of major loops in the transition graph as well as the number of states $ \mathcal{R} $ constituting the main hysteresis loop and its nested subloops. We find that $ \mathcal{R} $ is equal to the number of increasing subsequences contained in the permutation $\rho$.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Statistics of firstpassage Brownian functionals
Satya N. Majumdar ^{1} Baruch Meerson
Satya N. Majumdar, Baruch Meerson. Statistics of firstpassage Brownian functionals. J.Stat.Mech., 2020, 2002 (2), pp.023202. ⟨10.1088/17425468/ab6844⟩. ⟨hal02497830⟩
We study the distribution of firstpassage functionals of the type where represents a Brownian motion (with or without drift) with diffusion constant D, starting at x 0 > 0, and t f is the firstpassage time to the origin. In the driftless case, we compute exactly, for all n > −2, the probability density . We show that has an essential singular tail as and a powerlaw tail as . The leading essential singular behavior for small A can be obtained using the optimal fluctuation method (OFM), which also predicts the optimal paths of the conditioned process in this limit. For the case with a drift toward the origin, where no exact solution is known for general n > −1, we show that the OFM successfully predicts the tails of the distribution. For it predicts the same essential singular tail as in the driftless case. For it predicts a stretched exponential tail for all n > 0. In the limit of large Péclet number , where is the drift velocity toward the origin, the OFM predicts an exact largedeviation scaling behavior, valid for all A: , where is the mean value of in this limit. We compute the rate function analytically for all n > −1. We show that, while for n > 0 the rate function is analytic for all z, it has a nonanalytic behavior at z = 1 for −1 < n < 0 which can be interpreted as a dynamical phase transition. The order of this transition is 2 for −1/2 < n < 0, while for −1 < n < −1/2 the order of transition is ; it changes continuously with n. We also provide an illuminating alternative derivation of the OFM result by using a WKBtype asymptotic perturbation theory for large . Finally, we employ the OFM to study the case of (drift away from the origin). We show that, when the process is conditioned on reaching the origin, the distribution of coincides with the distribution of for with the same .
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Stochastic growth in timedependent environments
Guillaume Barraquand ^{1} Pierre Le Doussal ^{1} Alberto Rosso ^{2}
Guillaume Barraquand, Pierre Le Doussal, Alberto Rosso. Stochastic growth in timedependent environments. Physical Review E , American Physical Society (APS), 2020, 101 (4), ⟨10.1103/PhysRevE.101.040101⟩. ⟨hal02565202⟩
We study the KardarParisiZhang (KPZ) growth equation in one dimension with a noise variance $c(t)$ depending on time. We find that for $c(t)\propto t^{\alpha}$ there is a transition at $\alpha=1/2$. When $\alpha>1/2$, the solution saturates at large times towards a nonuniversal limiting distribution. When $\alpha<1/2$ the fluctuation field is governed by scaling exponents depending on $\alpha$ and the limiting statistics are similar to the case when $c(t)$ is constant. We investigate this problem using different methods: (1) Elementary changes of variables mapping the time dependent case to variants of the KPZ equation with constant variance of the noise but in a deformed potential (2) An exactly solvable discretization, the loggamma polymer model (3) Numerical simulations.
 1. Champs Aléatoires et Systèmes hors d'Équilibre
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Swimmer Suspensions on Substrates: Anomalous Stability and LongRange Order
Ananyo Maitra ^{1, 2} Pragya SrivastavaM. Cristina MarchettiSriram RamaswamyMartin Lenz ^{2, 3}
Ananyo Maitra, Pragya Srivastava, M. Cristina Marchetti, Sriram Ramaswamy, Martin Lenz. Swimmer Suspensions on Substrates: Anomalous Stability and LongRange Order. Phys.Rev.Lett., 2020, 124 (2), pp.028002. ⟨10.1103/PhysRevLett.124.028002⟩. ⟨hal02475283⟩
We present a comprehensive theory of the dynamics and fluctuations of a twodimensional suspension of polar active particles in an incompressible fluid confined to a substrate. We show that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation (or growth) rate for angular fluctuations, not parallel to the ordering direction, at zero wave number. This screening of the brokensymmetry mode in the stable state does lead to conventional rather than giant number fluctuations as argued by Bricard et al., Nature 503, 95 (2013), but their bend instability in a splaystable flock does not exist and the polar phase has longrange order in two dimensions. Our theory also describes confined threedimensional thinfilm suspensions of active polar particles as well as dense compressible active polar rods, and predicts a flocking transition without a banding instability.
 1. LJP  Laboratoire Jean Perrin
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 3. ESPCI ParisTech

Archive ouverte HAL – Symmetries in $B \to D^* \ell \nu$ angular observables
Marcel AlgueróSébastien DescotesGenon ^{1} Joaquim MatiasMartín NovoaBrunet ^{2}
Marcel Algueró, Sébastien DescotesGenon, Joaquim Matias, Martín NovoaBrunet. Symmetries in $B \to D^* \ell \nu$ angular observables. JHEP, 2020, 06, pp.156. ⟨10.1007/JHEP06(2020)156⟩. ⟨hal02518081⟩
We apply the formalism of amplitude symmetries to the angular distribution of the decays B → D$^{∗}$ℓν for ℓ = e, μ, τ . We show that the angular observables used to describe the distribution of this class of decays are not independent in absence of New Physics contributing to tensor operators. We derive sets of relations among the angular coefficients of the decay distribution for the massless and massive lepton cases which can be used to probe in a very general way the consistency among the angular observables and the underlying New Physics at work. We use these relations to access the longitudinal polarisation fraction of the D$^{∗}$ using different angular coefficients from the ones used by Belle experiment. This in the near future can provide an alternative strategy to measure $ {F}_L^{D\ast } $ in B → D$^{∗}$τν and to understand the relatively high value measured by the Belle experiment. Using the same symmetries, we identify three observables which may exhibit a tension if the experimental value of $ {F}_L^{D\ast } $ remains high. We discuss how these relations can be exploited for binned measurements. We also propose a new observable that could test for specific scenarios of New Physics generated by light righthanded neutrinos. Finally we study the prospects of testing these relations based on the projected experimental sensitivity of new experiments.
 1. IJCLab  Laboratoire de Physique des 2 Infinis Irène JoliotCurie
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – The convex hull of the runandtumble particle in a plane
Alexander K HartmannSatya N Majumdar ^{1} Hendrik Schawe ^{2} Gregory Schehr ^{1} Alexander Hartmann ^{2} Satya Majumdar ^{1}
Alexander K Hartmann, Satya N Majumdar, Hendrik Schawe, Gregory Schehr, Alexander Hartmann, et al.. The convex hull of the runandtumble particle in a plane. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2020, 2020 (5), pp.053401. ⟨10.1088/17425468/ab7c5f⟩. ⟨hal02881103⟩
We study the statistical properties of the convex hull of a planar runandtumble particle (RTP), also known as the "persistent random walk", where the particle/walker runs ballistically between tumble events at which it changes its direction randomly. We consider two different statistical ensembles where we either fix (i) the total number of tumblings $n$ or (ii) the total duration $t$ of the time interval. In both cases, we derive exact expressions for the average perimeter of the convex hull and then compare to numerical estimates finding excellent agreement. Further, we numerically compute the full distribution of the perimeter using Markov chain Monte Carlo techniques, in both ensembles, probing the far tails of the distribution, up to a precision smaller than $10^{100}$. This also allows us to characterize the rare events that contribute to the tails of these distributions.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. University of Oldenburg

Archive ouverte HAL – The influence of the brittleductile transition zone on aftershock and foreshock occurrence
Giuseppe Petrillo ^{1} Eugenio Lippiello ^{1} François Landes ^{2} Alberto Rosso ^{3}
Giuseppe Petrillo, Eugenio Lippiello, François Landes, Alberto Rosso. The influence of the brittleductile transition zone on aftershock and foreshock occurrence. Nature Communications, Nature Publishing Group, 2020. ⟨hal02908552⟩
Aftershock occurrence is characterized by scaling behaviors with quite universal exponents. At the same time, deviations from universality have been proposed as a tool to discriminate aftershocks from foreshocks. Here we show that the change in rheological behavior of the crust, from velocity weakening to velocity strengthening, represents a viable mechanism to explain statistical features of both aftershocks and foreshocks. More precisely, we present a model of the seismic fault described as a velocity weakening elastic layer coupled to a velocity strengthening viscoelastic layer. We show that the statistical properties of aftershocks in instrumental catalogs are recovered at a quantitative level, quite independently of the value of model parameters. We also find that large earthquakes are often anticipated by a preparatory phase characterized by the occurrence of foreshocks. Their magnitude distribution is significantly flatter than the aftershock one, in agreement with recent results for forecasting tools based on foreshocks.
 1. Department of Mathematics and Physics [Caserta]
 2. LRI  Laboratoire de Recherche en Informatique
 3. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Three and fourpoint connectivities of twodimensional critical $Q$ Potts random clusters on the torus
Nina Javerzat ^{1} Marco Picco ^{2} Raoul Santachiara ^{1}
Nina Javerzat, Marco Picco, Raoul Santachiara. Three and fourpoint connectivities of twodimensional critical $Q$ Potts random clusters on the torus. J.Stat.Mech., 2020, 2005, pp.053106. ⟨10.1088/17425468/ab7c5e⟩. ⟨hal02416915⟩
In a recent paper, we considered the effects of the torus lattice topology on the twopoint connectivity of QPotts clusters. These effects are universal and probe nontrivial structure constants of the theory. We complete here this work by considering the torus corrections to the three and fourpoint connectivities. These corrections, which depend on the scale invariant ratios of the triangle and quadrilateral formed by the three and four given points, test other nontrivial structure constants. We also present results of Monte Carlo simulations in good agreement with our predictions.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. LPTHE  Laboratoire de Physique Théorique et Hautes Energies

Archive ouverte HAL – Two anyons on the sphere: nonlinear states and spectrum
Alexios P. PolychronakosStéphane Ouvry ^{1}
Alexios P. Polychronakos, Stéphane Ouvry. Two anyons on the sphere: nonlinear states and spectrum. Nucl.Phys.B, 2020, 951, pp.114906. ⟨10.1016/j.nuclphysb.2019.114906⟩. ⟨hal02340259⟩
We study the energy spectrum of two anyons on the sphere in a constant magnetic field. Making use of rotational invariance we reduce the energy eigenvalue equation to a system of linear differential equations for functions of a single variable, a reduction analogous to separating center of mass and relative coordinates on the plane. We solve these equations by a generalization of the Frobenius method and derive numerical results for the energies of nonanalytically derivable states.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Universal gap statistics for random walks for a class of jump densities
Matteo Battilana ^{1} Satya N. Majumdar ^{1} Gregory Schehr ^{1}
Matteo Battilana, Satya N. Majumdar, Gregory Schehr. Universal gap statistics for random walks for a class of jump densities. Markov Processes And Related Fields, Polymat Publishing Company, 2020. ⟨hal02518812⟩
We study the order statistics of a random walk (RW) of $n$ steps whose jumps are distributed according to symmetric Erlang densities $f_p(\eta)\sim \eta^p \,e^{\eta}$, parametrized by a nonnegative integer $p$. Our main focus is on the statistics of the gaps $d_{k,n}$ between two successive maxima $d_{k,n}=M_{k,n}M_{k+1,n}$ where $M_{k,n}$ is the $k$th maximum of the RW between step 1 and step $n$. In the limit of large $n$, we show that the probability density function of the gaps $P_{k,n}(\Delta) = \Pr(d_{k,n} = \Delta)$ reaches a stationary density $P_{k,n}(\Delta) \to p_k(\Delta)$. For large $k$, we demonstrate that the typical fluctuations of the gap, for $d_{k,n}= O(1/\sqrt{k})$ (and $n \to \infty$), are described by a nontrivial scaling function that is independent of $k$ and of the jump probability density function $f_p(\eta)$, thus corroborating our conjecture about the universality of the regime of typical fluctuations (see G. Schehr, S. N. Majumdar, Phys. Rev. Lett. 108, 040601 (2012)). We also investigate the large fluctuations of the gap, for $d_{k,n} = O(1)$ (and $n \to \infty$), and show that these two regimes of typical and large fluctuations of the gaps match smoothly.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Archive ouverte HAL – Universal Scaling of the Velocity Field in Crack Front Propagation
Clément Le Priol ^{1} Pierre Le Doussal ^{2} Laurent Ponson ^{3} Alberto Rosso ^{4} Julien Chopin ^{5}
Clément Le Priol, Pierre Le Doussal, Laurent Ponson, Alberto Rosso, Julien Chopin. Universal Scaling of the Velocity Field in Crack Front Propagation. Physical Review Letters, American Physical Society, 2020, 124 (6), ⟨10.1103/PhysRevLett.124.065501⟩. ⟨hal02512228⟩
The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an outofequilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are however difficult to characterize in experiments at finite drive. Here we show that the correlation functions of the velocity field along the front allow to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient and can be extended to all systems displaying avalanche dynamics.
 1. LPENS (UMR_8023)  Laboratoire de physique de l'ENS  ENS Paris
 2. Champs Aléatoires et Systèmes hors d'Équilibre
 3. DALEMBERT  Institut Jean Le Rond d'Alembert
 4. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 5. IFUFB  Instituto de Fisica, Universidade Federal da Bahia

Archive ouverte HAL – Universal Survival Probability for a d Dimensional RunandTumble Particle
Francesco Mori ^{1} Pierre Le Doussal ^{2} Satya N. Majumdar ^{1} Satya Majumdar ^{1} Gregory Schehr ^{1}
Francesco Mori, Pierre Le Doussal, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Universal Survival Probability for a d Dimensional RunandTumble Particle. Physical Review Letters, American Physical Society, 2020, 124 (9), ⟨10.1103/PhysRevLett.124.090603⟩. ⟨hal02512214⟩
We consider an active runandtumble particle (RTP) in $d$ dimensions and compute exactly the probability $S(t)$ that the $x$component of the position of the RTP does not change sign up to time $t$. When the tumblings occur at a constant rate, we show that $S(t)$ is independent of $d$ for any finite time $t$ (and not just for large $t$), as a consequence of the celebrated Sparre Andersen theorem for discretetime random walks in one dimension. Moreover, we show that this universal result holds for a much wider class of RTP models in which the speed $v$ of the particle after each tumbling is random, drawn from an arbitrary probability distribution. We further demonstrate, as a consequence, the universality of the record statistics in the RTP problem.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. Champs Aléatoires et Systèmes hors d'Équilibre

Archive ouverte HAL – Velocity and diffusion constant of an active particle in a onedimensional force field
Pierre Le Doussal ^{1} Satya N. Majumdar ^{2} Satya Majumdar ^{2} Gregory Schehr ^{2}
Pierre Le Doussal, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Velocity and diffusion constant of an active particle in a onedimensional force field. EPL  Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2020, 130 (4), pp.40002. ⟨10.1209/02955075/130/40002⟩. ⟨hal02881224⟩
We consider a run an tumble particle with two velocity states $\pm v_0$, in an inhomogeneous force field $f(x)$ in one dimension. We obtain exact formulae for its velocity $V_L$ and diffusion constant $D_L$ for arbitrary periodic $f(x)$ of period $L$. They involve the "active potential" which allows to define a global bias. Upon varying parameters, such as an external force $F$, the dynamics undergoes transitions from nonergodic trapped states, to various moving states, some with non analyticities in the $V_L$ versus $F$ curve. A random landscape in the presence of a bias leads, for large $L$, to anomalous diffusion $x \sim t^\mu$, $\mu<1$, or to a phase with a finite velocity that we calculate.
 1. Champs Aléatoires et Systèmes hors d'Équilibre
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Asymptotic behavior of the length of the longest increasing subsequences of random walks – Archive ouverte HAL
J. Ricardo G. Mendonça ^{1} Hendrik Schawe ^{2} Alexander K. Hartmann ^{3} Alexander Hartmann
J. Ricardo G. Mendonça, Hendrik Schawe, Alexander K. Hartmann, Alexander Hartmann. Asymptotic behavior of the length of the longest increasing subsequences of random walks. Physical Review E , American Physical Society (APS), 2020, 101 (3), ⟨10.1103/PhysRevE.101.032102⟩. ⟨hal02512208⟩
We numerically estimate the leading asymptotic behavior of the length $L_{n}$ of the longest increasing subsequence of random walks with step increments following Student's $t$distribution with parameter in the range $1/2 \leq \nu \leq 5$. We find that the expected value $\mathbb{E}(L_{n}) \sim n^{\theta}\ln{n}$ with $\theta$ decreasing from $\theta(\nu=1/2) \approx 0.70$ to $\theta(\nu \geq 5/2) \approx 0.50$. For random walks with distribution of step increments of finite variance ($\nu > 2$), this confirms previous observation of $\mathbb{E}(L_{n}) \sim \sqrt{n}\ln{n}$ to leading order. We note that this asymptotic behavior (including the subleading term) resembles that of the largest part of random integer partitions under the uniform measure and that, curiously, both random variables seem to follow Gumbel statistics. We also provide more refined estimates for the asymptotic behavior of $\mathbb{E}(L_{n})$ for random walks with step increments of finite variance.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. University of Oldenburg
 3. Institut für Physik

Chaosassisted tunneling resonances in a synthetic Floquet superlattice – Archive ouverte HAL
Maxime Arnal ^{1} Gabriel Chatelain ^{1} Maxime Martinez ^{2} Nathan Dupont ^{1} Olivier Giraud ^{3} D. Ullmo ^{3} Bertrand Georgeot ^{2} Gabriel Lemarié ^{2} Juliette Billy ^{1} David GuéryOdelin ^{1}
Maxime Arnal, Gabriel Chatelain, Maxime Martinez, Nathan Dupont, Olivier Giraud, et al.. Chaosassisted tunneling resonances in a synthetic Floquet superlattice. Science Advances, 2020, 6 (38), pp.eabc4886. ⟨10.1126/sciadv.abc4886⟩. ⟨hal02534927⟩
The field of quantum simulation, which aims at using a tunable quantum system to simulate another, has been developing fast in the past years as an alternative to the allpurpose quantum computer. In particular, the use of temporal driving has attracted a huge interest recently as it was shown that certain fast drivings can create new topological effects, while a strong driving leads to e.g. Anderson localization physics. In this work, we focus on the intermediate regime to observe a quantum chaos transport mechanism called chaosassisted tunneling which provides new possibilities of control for quantum simulation. Indeed, this regime generates a rich classical phase space where stable trajectories form islands surrounded by a large sea of unstable chaotic orbits. This mimics an effective superlattice for the quantum states localized in the regular islands, with new controllable tunneling properties. Besides the standard textbook tunneling through a potential barrier, chaosassisted tunneling corresponds to a much richer tunneling process where the coupling between quantum states located in neighboring regular islands is mediated by other states spread over the chaotic sea. This process induces sharp resonances where the tunneling rate varies by orders of magnitude over a short range of parameters. We experimentally demonstrate and characterize these resonances for the first time in a quantum system. This opens the way to new kinds of quantum simulations with longrange transport and new types of control of quantum systems through complexity.
 1. Atomes Froids (LCAR)
 2. Information et Chaos Quantiques (LPT)
 3. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Collective excitations of a onedimensional quantum droplet – Archive ouverte HAL
Marek TylutkiGrigori E. AstrakharchikBoris A. Malomed ^{1} Dmitry S. Petrov ^{2} Grigori Astrakharchik ^{3} Boris Malomed ^{4} Dmitry Petrov
Marek Tylutki, Grigori E. Astrakharchik, Boris A. Malomed, Dmitry S. Petrov, Grigori Astrakharchik, et al.. Collective excitations of a onedimensional quantum droplet. Physical Review A, American Physical Society 2020, 101 (5), ⟨10.1103/PhysRevA.101.051601⟩. ⟨hal02881226⟩
We calculate the excitation spectrum of a onedimensional selfbound quantum droplet in a twocomponent bosonic mixture described by the GrossPitaevskii equation (GPE) with cubic and quadratic nonlinearities. The cubic term originates from the meanfield energy of the mixture proportional to the effective coupling constant $\delta g$, whereas the quadratic nonlinearity corresponds to the attractive beyondmeanfield contribution. The droplet properties are governed by a control parameter $\gamma\propto \delta g N^{2/3}$, where $N$ is the particle number. For large $\gamma>0$ the droplet features the flattop shape with the discrete part of its spectrum consisting of planewave Bogoliubov phonons propagating through the flatdensity bulk and reflected by edges of the droplet. With decreasing $\gamma$ these modes cross into the continuum, sequentially crossing the particleemission threshold at specific critical values. A notable exception is the breathing mode which we find to be always bound. The balance point $\gamma = 0$ provides implementation of a system governed by the GPE with an unusual quadratic nonlinearity. This case is characterized by the ratio of the breathingmode frequency to the particleemission threshold equal to 0.8904. As $\gamma$ tends to $\infty$ this ratio tends to 1 and the droplet transforms into the soliton solution of the integrable cubic GPE.
 1. Tel Aviv University [Tel Aviv]
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 3. UPC  Universitat Politècnica de Catalunya [BarcelonaTech]
 4. Department of Interdisciplinary Studies

Comment on “Effective Confining Potential of Quantum States in Disordered Media” – Archive ouverte HAL
Alain Comtet ^{1} Christophe Texier ^{1}
Alain Comtet, Christophe Texier. Comment on “Effective Confining Potential of Quantum States in Disordered Media”. Physical Review Letters, American Physical Society, 2020, 124 (21), ⟨10.1103/PhysRevLett.124.219701⟩. ⟨hal02881221⟩
We provide some analytical tests of the density of states estimation from the "localization landscape" approach of Ref. [Phys. Rev. Lett. 116, 056602 (2016)]. We consider two different solvable models for which we obtain the distribution of the landscape function and argue that the precise spectral singularities are not reproduced by the estimation of the landscape approach.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Critical energy landscape of linear soft spheres – Archive ouverte HAL
Silvio Franz ^{1} Antonio Sclocchi ^{1} Pierfrancesco Urbani ^{2}
Silvio Franz, Antonio Sclocchi, Pierfrancesco Urbani. Critical energy landscape of linear soft spheres. SciPost Physics, SciPost Foundation, 2020. ⟨hal02908534⟩
We show that soft spheres interacting with a linear ramp potential when overcompressed beyond the jamming point fall in an amorphous solid phase which is critical, mechanically marginally stable and share many features with the jamming point itself. In the whole phase, the relevant local minima of the potential energy landscape display an isostatic contact network of perfectly touching spheres whose statistics is controlled by an infinite lengthscale. Excitations around such energy minima are nonlinear, system spanning, and characterized by a set of nontrivial critical exponents. We perform numerical simulations to measure their values and show that, while they coincide, within numerical precision, with the critical exponents appearing at jamming, the nature of the corresponding excitations is richer. Therefore, linear soft spheres appear as a novel class of finite dimensional systems that selforganize into new, critical, marginally stable, states.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. IPHT  Institut de Physique Théorique  UMR CNRS 3681

Current fluctuations in noninteracting runandtumble particles in one dimension – Archive ouverte HAL
Tirthankar Banerjee ^{1} Satya N. Majumdar ^{1} Alberto Rosso ^{1} Satya Majumdar ^{1} Gregory Schehr ^{1}
Tirthankar Banerjee, Satya N. Majumdar, Alberto Rosso, Satya Majumdar, Gregory Schehr. Current fluctuations in noninteracting runandtumble particles in one dimension. Physical Review E , American Physical Society (APS), 2020, 101 (5), ⟨10.1103/PhysRevE.101.052101⟩. ⟨hal02565189⟩
We present a general framework to study the distribution of the flux through the origin up to time $t$, in a noninteracting onedimensional system of particles with a step initial condition with a fixed density $\rho$ of particles to the left of the origin. We focus principally on two cases: (i) when the particles undergo diffusive dynamics (passive case) and (ii) runandtumble dynamics for each particle (active case). In analogy with disordered systems, we consider the flux distribution both for the annealed and the quenched initial conditions, for the passive and active particles. In the annealed case, we show that, for arbitrary particle dynamics, the flux distribution is a Poissonian with a mean $\mu(t)$ that we compute exactly in terms of the Green's function of the single particle dynamics. For the quenched case, we show that, for the runandtumble dynamics, the quenched flux distribution takes an anomalous large deviation form at large times $P_{\rm qu}(Q,t) \sim \exp\left[\rho\, v_0\, \gamma \, t^2 \psi_{\rm RTP}\left(\frac{Q}{\rho v_0\,t} \right) \right]$, where $\gamma$ is the rate of tumbling and $v_0$ is the ballistic speed between two successive tumblings. In this paper, we compute the rate function $\psi_{\rm RTP}(q)$ and show that it is nontrivial. Our method also gives access to the probability of the rare event that, at time $t$, there is no particle to the right of the origin. For diffusive and runandtumble dynamics, we find that this probability decays with time as a stretched exponential, $\sim \exp(c\, \sqrt{t})$ where the constant $c$ can be computed exactly. We verify our results for these large deviations by using an importance sampling MonteCarlo method.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Dispersionless evolution of inviscid nonlinear pulses – Archive ouverte HAL
M. Isoard ^{1} N. Pavloff ^{1} A. M. Kamchatnov ^{2}
M. Isoard, N. Pavloff, A. M. Kamchatnov. Dispersionless evolution of inviscid nonlinear pulses. EPL  Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2020. ⟨hal02565206⟩
We consider the onedimensional dynamics of nonlinear nondispersive waves. The problem can be mapped onto a linear one by means of the hodograph transform. We propose an approximate scheme for solving the corresponding EulerPoisson equation which is valid for any kind of nonlinearity. The approach is exact for monoatomic classical gas and agrees very well with exact results and numerical simulations for other systems. We also provide a simple and accurate determination of the wave breaking time for typical initial conditions.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. Institute of Spectroscopy

Distribution of the time between maximum and minimum of random walks – Archive ouverte HAL
Francesco Mori ^{1} Satya N. Majumdar ^{1} Satya Majumdar ^{1} Gregory Schehr ^{1}
Francesco Mori, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Distribution of the time between maximum and minimum of random walks. Physical Review E , American Physical Society (APS), 2020, 101 (5), ⟨10.1103/PhysRevE.101.052111⟩. ⟨hal02881215⟩
We consider a onedimensional Brownian motion of fixed duration $T$. Using a pathintegral technique, we compute exactly the probability distribution of the difference $\tau=t_{\min}t_{\max}$ between the time $t_{\min}$ of the global minimum and the time $t_{\max}$ of the global maximum. We extend this result to a Brownian bridge, i.e. a periodic Brownian motion of period $T$. In both cases, we compute analytically the first few moments of $\tau$, as well as the covariance of $t_{\max}$ and $t_{\min}$, showing that these times are anticorrelated. We demonstrate that the distribution of $\tau$ for Brownian motion is valid for discretetime random walks with $n$ steps and with a finite jump variance, in the limit $n\to \infty$. In the case of L\'evy flights, which have a divergent jump variance, we numerically verify that the distribution of $\tau$ differs from the Brownian case. For random walks with continuous and symmetric jumps we numerically verify that the probability of the event "$\tau = n$" is exactly $1/(2n)$ for any finite $n$, independently of the jump distribution. Our results can be also applied to describe the distance between the maximal and minimal height of $(1+1)$dimensional stationarystate KardarParisiZhang interfaces growing over a substrate of finite size $L$. Our findings are confirmed by numerical simulations. Some of these results have been announced in a recent Letter [Phys. Rev. Lett. 123, 200201 (2019)].
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Extreme value statistics of correlated random variables: a pedagogical review – Archive ouverte HAL
Satya N. Majumdar ^{1} Arnab PalGregory Schehr ^{1}
Satya N. Majumdar, Arnab Pal, Gregory Schehr. Extreme value statistics of correlated random variables: a pedagogical review. Physics Reports, Elsevier, 2020, ⟨10.10667⟩. ⟨hal02512248⟩
Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any timeseries and has applications in climate, finance, sports, all the way to physics of disordered systems where one is interested in the statistics of the ground state energy. While the EVS of `uncorrelated' variables are well understood, little is known for strongly correlated random variables. Only recently this subject has gained much importance both in statistical physics and in probability theory. In this review, we will first recall the classical EVS for uncorrelated variables and discuss the three universality classes of extreme value limiting distribution, known as the Gumbel, Fr\'echet and Weibull distribution. We then show that, for weakly correlated random variables with a finite correlation length/time, the limiting extreme value distribution can still be inferred from that of the uncorrelated variables using a renormalisation grouplike argument. Finally, we consider the most interesting examples of strongly correlated variables for which there are very few exact results for the EVS. We discuss few examples of such strongly correlated systems (such as the Brownian motion and the eigenvalues of a random matrix) where some analytical progress can be made. We also discuss other observables related to extremes, such as the density of nearextreme events, time at which an extreme value occurs, order and record statistics, etc.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Fewbody bound states of twodimensional bosons – Archive ouverte HAL
G. Guijarro ^{1} G. E. Astrakharchik ^{1} J. Boronat ^{1} B. BazakD. S. Petrov ^{2}
G. Guijarro, G. E. Astrakharchik, J. Boronat, B. Bazak, D. S. Petrov. Fewbody bound states of twodimensional bosons. Physical Review A, American Physical Society 2020, ⟨10.1103/PhysRevA.101.041602⟩. ⟨hal02537195⟩
We study clusters of the type A$_N$B$_M$ with $N\leq M\leq 3$ in a twodimensional mixture of A and B bosons, with attractive AB and equally repulsive AA and BB interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths $a_{AB}$ and $a_{AA}=a_{BB}$, for sufficiently large attractiontorepulsion ratios $a_{AB}/a_{BB}$. When $a_{AB}/a_{BB}$ decreases below $\approx 10$, the dimerdimer interaction changes from attractive to repulsive and the populationbalanced AABB and AAABBB clusters break into AB dimers. Calculating the AAABBB hexamer energy just below this threshold, we find an effective threedimer repulsion which may have important implications for the manybody problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The populationimbalanced ABB trimer, ABBB tetramer, and AABBB pentamer remain bound beyond the dimerdimer threshold. In the dipolar model, they break up at $a_{AB}\approx 2 a_{BB}$ where the atomdimer interaction switches to repulsion.
 1. UPC  Universitat Politècnica de Catalunya [Barcelona]
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions – Archive ouverte HAL
Etienne GranetMaurizio Fagotti ^{1} Fabian H.L. Essler
Etienne Granet, Maurizio Fagotti, Fabian H.L. Essler. Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions. SciPost Phys., 2020, 9 (3), pp.033. ⟨10.21468/SciPostPhys.9.3.033⟩. ⟨hal02542815⟩
We consider the problems of calculating the dynamical order parameter twopoint function at finite temperatures and the onepoint function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semilocal operators in interacting integrable models.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Finitetime adiabatic processes: Derivation and speed limit – Archive ouverte HAL
Carlos Plata ^{1} David GuéryOdelin ^{2} Emmanuel Trizac ^{3} Antonio Prados ^{4}
Carlos Plata, David GuéryOdelin, Emmanuel Trizac, Antonio Prados. Finitetime adiabatic processes: Derivation and speed limit. Physical Review E , American Physical Society (APS), 2020, 101 (3), ⟨10.1103/PhysRevE.101.032129⟩. ⟨hal02535447⟩
Obtaining adiabatic processes that connect equilibrium states in a given time represents a challenge for mesoscopic systems. In this paper, we explicitly show how to build these finitetime adiabatic processes for an overdamped Brownian particle in an arbitrary potential, a system that is relevant both at the conceptual and the practical level. This is achieved by jointly engineering the time evolutions of the binding potential and the fluid temperature. Moreover, we prove that the second principle imposes a speed limit for such adiabatic transformations: there appears a minimum time to connect the initial and final states. This minimum time can be explicitly calculated for a general compression/decompression situation.
 1. Padova University
 2. Atomes Froids (LCAR)
 3. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 4. Universidad de Sevilla

LastPassage Time for Linear Diffusions and Application to the Emptying Time of a Box – Archive ouverte HAL
Alain Comtet ^{1} Françoise Cornu ^{1} Grégory Schehr ^{1}
Alain Comtet, Françoise Cornu, Grégory Schehr. LastPassage Time for Linear Diffusions and Application to the Emptying Time of a Box. Journal of Statistical Physics, Springer Verlag, 2020, ⟨10.1007/s10955020026376⟩. ⟨hal02988500⟩
We study the statistics of lastpassage time for linear diffusions. First we present an elementary derivation of the Laplace transform of the probability density of the lastpassage time, thus recovering known results from the mathematical literature. We then illustrate them on several explicit examples. In a second step we study the spectral properties of the Schr\"{o}dinger operator associated to such diffusions in an even potential $U(x) = U(x)$, unveiling the role played by the socalled Weyl coefficient. Indeed, in this case, our approach allows us to relate the lastpassage times for dual diffusions (i.e., diffusions driven by opposite force fields) and to obtain new explicit formulae for the mean lastpassage time. We further show that, for such even potentials, the small time $t$ expansion of the mean lastpassage time on the interval $[0,t]$ involves the Kortevegde Vries invariants, which are well known in the theory of Schr\"odinger operators. Finally, we apply these results to study the emptying time of a onedimensional box, of size $L$, containing $N$ independent Brownian particles subjected to a constant drift. In the scaling limit where both $N \to \infty$ and $L \to \infty$, keeping the density $\rho = N/L$ fixed, we show that the limiting density of the emptying time is given by a Gumbel distribution. Our analysis provides a new example of the applications of extreme value statistics to outofequilibrium systems.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Lattice walk area combinatorics, some remarkable trigonometric sums and Apérylike numbers – Archive ouverte HAL
Stéphane Ouvry ^{1} Alexios Polychronakos
Stéphane Ouvry, Alexios Polychronakos. Lattice walk area combinatorics, some remarkable trigonometric sums and Apérylike numbers. Nucl.Phys.B, 2020, 960, pp.115174. ⟨10.1016/j.nuclphysb.2020.115174⟩. ⟨hal02886896⟩
Explicit algebraic area enumeration formulae are derived for various lattice walks generalizing the canonical square lattice walks, and in particular for the triangular lattice chiral walks recently introduced by the authors. A key element in the enumeration is the derivation of some identities involving some remarkable trigonometric sums –which are also important building blocks of non trivial quantum models such as the Hofstadter model– and their explicit rewriting in terms of multiple binomial sums. An intriguing connection is also made with number theory and some classes of Apérylike numbers, the cousins of the Apéry numbers which play a central role in irrationality considerations for ζ(2) and ζ(3) .
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Mapping and Modeling the Nanomechanics of Bare and ProteinCoated Lipid Nanotubes – Archive ouverte HAL
Guillaume Lamour ^{1} Antoine Allard ^{1, 2} Juan Pelta ^{1} Sid Labdi ^{1} Martin Lenz ^{3} Clément Campillo ^{1}
Guillaume Lamour, Antoine Allard, Juan Pelta, Sid Labdi, Martin Lenz, et al.. Mapping and Modeling the Nanomechanics of Bare and ProteinCoated Lipid Nanotubes. Physical Review X, American Physical Society, 2020, 10 (1), pp.011031. ⟨10.1103/PhysRevX.10.011031⟩. ⟨hal02512272⟩
Membrane nanotubes are continuously assembled and disassembled by the cell to generate and dispatch transport vesicles, for instance, in endocytosis. While these processes crucially involve the illunderstood local mechanics of the nanotube, existing micromanipulation assays only give access to its global mechanical properties. Here we develop a new platform to study this local mechanics using atomic force microscopy (AFM). On a single coverslip we quickly generate millions of substratebound nanotubes, out of which dozens can be imaged by AFM in a single experiment. A full theoretical description of the AFM tipmembrane interaction allows us to accurately relate AFM measurements of the nanotube heights, widths, and rigidities to the membrane bending rigidity and tension, thus demonstrating our assay as an accurate probe of nanotube mechanics. We reveal a universal relationship between nanotube height and rigidity, which is unaffected by the specific conditions of attachment to the substrate. Moreover, we show that the parabolic shape of forcedisplacement curves results from thermal fluctuations of the membrane that collides intermittently with the AFM tip. We also show that membrane nanotubes can exhibit high resilience against extreme lateral compression. Finally, we mimic in vivo actin polymerization on nanotubes and use AFM to assess the induced changes in nanotube physical properties. Our assay may help unravel the local mechanics of membraneprotein interactions, including membrane remodeling in nanotube scission and vesicle formation.
 1. LAMBE  UMR 8587  Laboratoire Analyse, Modélisation et Matériaux pour la Biologie et l'Environnement
 2. PCC  PhysicoChimieCurie
 3. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Multicomponent colloidal gels: interplay between structure and mechanical properties – Archive ouverte HAL
Claudia FerreiroCordovaMehdi Bouzid ^{1} Emanuela del GadoGiuseppe Foffi ^{2} Claudia FerreiroCórdova
Claudia FerreiroCordova, Mehdi Bouzid, Emanuela del Gado, Giuseppe Foffi, Claudia FerreiroCórdova. Multicomponent colloidal gels: interplay between structure and mechanical properties. Soft Matter, Royal Society of Chemistry, 2020, 16 (18), pp.44144421. ⟨10.1039/C9SM02410G⟩. ⟨hal02881157⟩
We present a detailed numerical study of multicomponent colloidal gels interacting sterically and obtained by arrested phase separation. Under deformation, we found that the interplay between the different intertwined networks is key. Increasing the number of component leads to softer solids that can accomodate progressively larger strain before yielding. The simulations highlight how this is the direct consequence of the purely repulsive interactions between the different components, which end up enhancing the linear response of the material. Our work {provides new insight into mechanisms at play for controlling the material properties and open the road to new design principles for} soft composite solids
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. LPS  Laboratoire de Physique des Solides

Numerical solution of the dynamical mean field theory of infinitedimensional equilibrium liquids – Archive ouverte HAL
Alessandro Manacorda ^{1} Gregory Schehr ^{2} Francesco Zamponi ^{1}
Alessandro Manacorda, Gregory Schehr, Francesco Zamponi. Numerical solution of the dynamical mean field theory of infinitedimensional equilibrium liquids. Journal of Chemical Physics, American Institute of Physics, 2020, 152 (16), pp.164506. ⟨10.1063/5.0007036⟩. ⟨hal02554137⟩
 1. Systèmes Désordonnés et Applications
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States – Archive ouverte HAL
John MartinStefan WeigertOlivier Giraud ^{1}
John Martin, Stefan Weigert, Olivier Giraud. Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States. Quantum, Verein, 2020. ⟨hal02881098⟩
Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closedform expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j=5. The closedform expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Optimizing Brownian escape rates by potential shaping – Archive ouverte HAL
Marie Chupeau ^{1} Jannes GladrowAlexei Chepelianskii ^{2} Ulrich F. KeyserEmmanuel Trizac ^{1} Ulrich Keyser
Marie Chupeau, Jannes Gladrow, Alexei Chepelianskii, Ulrich F. Keyser, Emmanuel Trizac, et al.. Optimizing Brownian escape rates by potential shaping. Proceedings of the National Academy of Sciences of the United States of America , National Academy of Sciences, 2020, 117 (3), pp.13831388. ⟨10.1073/pnas.1910677116⟩. ⟨hal02512216⟩
Brownian escape is key to a wealth of physicochemical processes, including polymer folding, and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with increasing barrier height. Here, we show experimentally that higher, finetuned barrier profiles result in significantly enhanced escape rates in breach of the intuition relying on the above scaling law, and address in theory the corresponding conditions for maximum speedup. Importantly, our barriers end on the same energy on which they start. For overdamped dynamics, the achievable boost of escape rates is, in principle, unbounded so that the barrier optimization has to be regularized. We derive optimal profiles under two different regularizations, and uncover the efficiency of Nshaped barriers. We then demonstrate the viability of such a potential in automated microfluidic Brownian dynamics experiments using holographic optical tweezers and achieve a doubling of escape rates compared to unhindered Brownian motion. Finally, we show that this escape rate boost extends into the lowfriction inertial regime.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. LPCT  Laboratoire de PhysicoChimie Théorique

Reversal of contractility as a signature of selforganization in cytoskeletal bundles – Archive ouverte HAL
Martin Lenz ^{1}
Martin Lenz. Reversal of contractility as a signature of selforganization in cytoskeletal bundles. eLife, eLife Sciences Publication, 2020, 9, ⟨10.7554/eLife.51751⟩. ⟨hal02518848⟩
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Rigorous bounds on dynamical response functions and timetranslation symmetry breaking – Archive ouverte HAL
Marko Medenjak ^{1} Tomaz Prosen ^{2} Lenart Zadnik ^{3}
Marko Medenjak, Tomaz Prosen, Lenart Zadnik. Rigorous bounds on dynamical response functions and timetranslation symmetry breaking. SciPost Physics, SciPost Foundation, 2020, 9 (1), ⟨10.21468/SciPostPhys.9.1.003⟩. ⟨hal02935659⟩
Dynamical response functions are standard tools for probing local physics near the equilibrium. They provide information about relaxation properties after the equilibrium state is weakly perturbed. In this paper we focus on systems which break the assumption of thermalization by exhibiting persistent temporal oscillations. We provide rigorous bounds on the Fourier components of dynamical response functions in terms of extensive or local dynamical symmetries, i.e., extensive or local operators with periodic time dependence. Additionally, we discuss the effects of spatially inhomogeneous dynamical symmetries. The bounds are explicitly implemented on the example of an interacting Floquet system, specifically in the integrable Trotterization of the Heisenberg XXZ model.
 1. IPM  institut de Physique Théorique Philippe Meyer
 2. FMF  Faculty of Mathematics and Physics [Ljubljana]
 3. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Scalable quantum computing with qudits on a graph – Archive ouverte HAL
E. O. Kiktenko ^{1} A. S. NikolaevaPeng XuG. V. Shlyapnikov ^{2} A. K. Fedorov ^{3}
E. O. Kiktenko, A. S. Nikolaeva, Peng Xu, G. V. Shlyapnikov, A. K. Fedorov. Scalable quantum computing with qudits on a graph. Physical Review A, American Physical Society 2020, 101 (2), ⟨10.1103/PhysRevA.101.022304⟩. ⟨hal02512218⟩
We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality of qudits and their topology of connections for a scalable multiqudit processor, where higher qudit levels are used for substituting ancillas. The suggested model is of importance for the realization of quantum algorithms and as a method of quantum error correction codes for singlequbit operations.
 1. IPE  Schmidt United Institute of Physics of the Earth [Moscow]
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 3. Russian Quantum Center

State transition graph of the Preisach model and the role of returnpoint memory – Archive ouverte HAL
M. Mert Terzi ^{1} Muhittin Mungan
M. Mert Terzi, Muhittin Mungan. State transition graph of the Preisach model and the role of returnpoint memory. Physical Review E, 2020, 102 (1), ⟨10.1103/PhysRevE.102.012122⟩. ⟨hal02908545⟩
The Preisach model has been useful as a nullmodel for understanding memory formation in periodically driven disordered systems. In amorphous solids for example, the athermal response to shear is due to localized plastic events (soft spots). As shown recently by one of us, the plastic response to applied shear can be rigorously described in terms of a directed network whose transitions correspond to one or more soft spots changing states. The topology of this graph depends on the interactions between softspots and when such interactions are negligible, the resulting description becomes that of the Preisach model. A first step in linking transition graph topology with the underlying softspot interactions is therefore to determine the structure of such graphs in the absence of interactions. Here we perform a detailed analysis of the transition graph of the Preisach model. We highlight the important role played by return point memory in organizing the graph into a hierarchy of loops and subloops. Our analysis reveals that the topology of a large portion of this graph is actually not governed by the values of the switching fields that describe the individual hysteretic behavior of the individual elements, but by a coarser parameter, a permutation $\rho$ which prescribes the sequence in which the individual hysteretic elements change their states as the main hysteresis loop is traversed. This in turn allows us to derive combinatorial properties, such as the number of major loops in the transition graph as well as the number of states $ \mathcal{R} $ constituting the main hysteresis loop and its nested subloops. We find that $ \mathcal{R} $ is equal to the number of increasing subsequences contained in the permutation $\rho$.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Statistics of the number of records for random walks and Lévy flights on a 1D lattice – Archive ouverte HAL
Philippe Mounaix ^{1} Satya Majumdar ^{2} Grégory Schehr ^{2}
Philippe Mounaix, Satya Majumdar, Grégory Schehr. Statistics of the number of records for random walks and Lévy flights on a 1D lattice. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2020, 53 (41), pp.415003. ⟨10.1088/17518121/abac97⟩. ⟨hal02958283⟩
We study the statistics of the number of records R n for a symmetric, nstep, discrete jump process on a 1D lattice. At a given step, the walker can jump by arbitrary lattice units drawn from a given symmetric probability distribution. This process includes, as a special case, the standard nearest neighbor lattice random walk. We derive explicitly the generating function of the distribution P (R n) of the number of records, valid for arbitrary discrete jump distributions. As a byproduct, we provide a relatively simple proof of the generalized Sparre Andersen theorem for the survival probability of a random walk on a line, with discrete or continuous jump distributions. For the discrete jump process, we then derive the asymptotic large n behavior of P (R n) as well as of the average number of records E(R n). We show that unlike the case of random walks with symmetric and continuous jump distributions where the record statistics is strongly universal (i.e., independent of the jump distribution for all n), the record statistics for lattice walks depends on the jump distribution for any fixed n. However, in the large n limit, we show that the distribution of the scaled record number R n /E(R n) approaches a universal, halfGaussian form for any discrete jump process. The dependence on the jump distribution enters only through the scale factor E(R n), which we also compute in the large n limit for arbitrary jump distributions. We present explicit results for a few examples and provide numerical checks of our analytical predictions.
 1. CPHT  Centre de Physique Théorique [Palaiseau]
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Stochastic growth in timedependent environments – Archive ouverte HAL
Guillaume Barraquand ^{1} Pierre Le Doussal ^{1} Alberto Rosso ^{2}
Guillaume Barraquand, Pierre Le Doussal, Alberto Rosso. Stochastic growth in timedependent environments. Physical Review E , American Physical Society (APS), 2020, 101 (4), ⟨10.1103/PhysRevE.101.040101⟩. ⟨hal02565202⟩
We study the KardarParisiZhang (KPZ) growth equation in one dimension with a noise variance $c(t)$ depending on time. We find that for $c(t)\propto t^{\alpha}$ there is a transition at $\alpha=1/2$. When $\alpha>1/2$, the solution saturates at large times towards a nonuniversal limiting distribution. When $\alpha<1/2$ the fluctuation field is governed by scaling exponents depending on $\alpha$ and the limiting statistics are similar to the case when $c(t)$ is constant. We investigate this problem using different methods: (1) Elementary changes of variables mapping the time dependent case to variants of the KPZ equation with constant variance of the noise but in a deformed potential (2) An exactly solvable discretization, the loggamma polymer model (3) Numerical simulations.
 1. Champs Aléatoires et Systèmes hors d'Équilibre
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Symmetries in $B \to D^* \ell \nu$ angular observables – Archive ouverte HAL
Marcel AlgueróSébastien DescotesGenon ^{1} Joaquim MatiasMartín NovoaBrunet ^{2}
Marcel Algueró, Sébastien DescotesGenon, Joaquim Matias, Martín NovoaBrunet. Symmetries in $B \to D^* \ell \nu$ angular observables. JHEP, 2020, 06, pp.156. ⟨10.1007/JHEP06(2020)156⟩. ⟨hal02518081⟩
We apply the formalism of amplitude symmetries to the angular distribution of the decays B → D$^{∗}$ℓν for ℓ = e, μ, τ . We show that the angular observables used to describe the distribution of this class of decays are not independent in absence of New Physics contributing to tensor operators. We derive sets of relations among the angular coefficients of the decay distribution for the massless and massive lepton cases which can be used to probe in a very general way the consistency among the angular observables and the underlying New Physics at work. We use these relations to access the longitudinal polarisation fraction of the D$^{∗}$ using different angular coefficients from the ones used by Belle experiment. This in the near future can provide an alternative strategy to measure $ {F}_L^{D\ast } $ in B → D$^{∗}$τν and to understand the relatively high value measured by the Belle experiment. Using the same symmetries, we identify three observables which may exhibit a tension if the experimental value of $ {F}_L^{D\ast } $ remains high. We discuss how these relations can be exploited for binned measurements. We also propose a new observable that could test for specific scenarios of New Physics generated by light righthanded neutrinos. Finally we study the prospects of testing these relations based on the projected experimental sensitivity of new experiments.
 1. IJCLab  Laboratoire de Physique des 2 Infinis Irène JoliotCurie
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

The convex hull of the runandtumble particle in a plane – Archive ouverte HAL
Alexander K HartmannSatya N Majumdar ^{1} Hendrik Schawe ^{2} Gregory Schehr ^{1} Alexander Hartmann ^{2} Satya Majumdar ^{1}
Alexander K Hartmann, Satya N Majumdar, Hendrik Schawe, Gregory Schehr, Alexander Hartmann, et al.. The convex hull of the runandtumble particle in a plane. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2020, 2020 (5), pp.053401. ⟨10.1088/17425468/ab7c5f⟩. ⟨hal02881103⟩
We study the statistical properties of the convex hull of a planar runandtumble particle (RTP), also known as the "persistent random walk", where the particle/walker runs ballistically between tumble events at which it changes its direction randomly. We consider two different statistical ensembles where we either fix (i) the total number of tumblings $n$ or (ii) the total duration $t$ of the time interval. In both cases, we derive exact expressions for the average perimeter of the convex hull and then compare to numerical estimates finding excellent agreement. Further, we numerically compute the full distribution of the perimeter using Markov chain Monte Carlo techniques, in both ensembles, probing the far tails of the distribution, up to a precision smaller than $10^{100}$. This also allows us to characterize the rare events that contribute to the tails of these distributions.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. University of Oldenburg

The influence of the brittleductile transition zone on aftershock and foreshock occurrence – Archive ouverte HAL
Giuseppe Petrillo ^{1} Eugenio Lippiello ^{1} François Landes ^{2} Alberto Rosso ^{3}
Giuseppe Petrillo, Eugenio Lippiello, François Landes, Alberto Rosso. The influence of the brittleductile transition zone on aftershock and foreshock occurrence. Nature Communications, Nature Publishing Group, 2020. ⟨hal02908552⟩
Aftershock occurrence is characterized by scaling behaviors with quite universal exponents. At the same time, deviations from universality have been proposed as a tool to discriminate aftershocks from foreshocks. Here we show that the change in rheological behavior of the crust, from velocity weakening to velocity strengthening, represents a viable mechanism to explain statistical features of both aftershocks and foreshocks. More precisely, we present a model of the seismic fault described as a velocity weakening elastic layer coupled to a velocity strengthening viscoelastic layer. We show that the statistical properties of aftershocks in instrumental catalogs are recovered at a quantitative level, quite independently of the value of model parameters. We also find that large earthquakes are often anticipated by a preparatory phase characterized by the occurrence of foreshocks. Their magnitude distribution is significantly flatter than the aftershock one, in agreement with recent results for forecasting tools based on foreshocks.
 1. Department of Mathematics and Physics [Caserta]
 2. LRI  Laboratoire de Recherche en Informatique
 3. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Topological effects and conformal invariance in longrange correlated random surfaces – Archive ouverte HAL
Nina Javerzat ^{1} Sebastian Grijalva ^{1} Alberto Rosso ^{1} Raoul Santachiara ^{1}
Nina Javerzat, Sebastian Grijalva, Alberto Rosso, Raoul Santachiara. Topological effects and conformal invariance in longrange correlated random surfaces. SciPost Phys., 2020, 9 (4), pp.050. ⟨10.21468/SciPostPhys.9.4.050⟩. ⟨hal02863162⟩
We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level $h$. The set of activated sites is usually denoted as the excursion set. The connected components of this set, the level clusters, define a oneparameter ($H$) family of percolation models with longrange correlation in the site occupation. The level clusters percolate at a finite value $h=h_c$ and for $H\leq\frac{3}{4}$ the phase transition is expected to remain in the same universality class of the pure (i.e. uncorrelated) percolation. For $\frac{3}{4}
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Universal gap statistics for random walks for a class of jump densities – Archive ouverte HAL
Matteo Battilana ^{1} Satya N. Majumdar ^{1} Gregory Schehr ^{1}
Matteo Battilana, Satya N. Majumdar, Gregory Schehr. Universal gap statistics for random walks for a class of jump densities. Markov Processes And Related Fields, Polymat Publishing Company, 2020. ⟨hal02518812⟩
We study the order statistics of a random walk (RW) of $n$ steps whose jumps are distributed according to symmetric Erlang densities $f_p(\eta)\sim \eta^p \,e^{\eta}$, parametrized by a nonnegative integer $p$. Our main focus is on the statistics of the gaps $d_{k,n}$ between two successive maxima $d_{k,n}=M_{k,n}M_{k+1,n}$ where $M_{k,n}$ is the $k$th maximum of the RW between step 1 and step $n$. In the limit of large $n$, we show that the probability density function of the gaps $P_{k,n}(\Delta) = \Pr(d_{k,n} = \Delta)$ reaches a stationary density $P_{k,n}(\Delta) \to p_k(\Delta)$. For large $k$, we demonstrate that the typical fluctuations of the gap, for $d_{k,n}= O(1/\sqrt{k})$ (and $n \to \infty$), are described by a nontrivial scaling function that is independent of $k$ and of the jump probability density function $f_p(\eta)$, thus corroborating our conjecture about the universality of the regime of typical fluctuations (see G. Schehr, S. N. Majumdar, Phys. Rev. Lett. 108, 040601 (2012)). We also investigate the large fluctuations of the gap, for $d_{k,n} = O(1)$ (and $n \to \infty$), and show that these two regimes of typical and large fluctuations of the gaps match smoothly.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques

Universal Scaling of the Velocity Field in Crack Front Propagation – Archive ouverte HAL
Clément Le Priol ^{1} Pierre Le Doussal ^{2} Laurent Ponson ^{3} Alberto Rosso ^{4} Julien Chopin ^{5}
Clément Le Priol, Pierre Le Doussal, Laurent Ponson, Alberto Rosso, Julien Chopin. Universal Scaling of the Velocity Field in Crack Front Propagation. Physical Review Letters, American Physical Society, 2020, 124 (6), ⟨10.1103/PhysRevLett.124.065501⟩. ⟨hal02512228⟩
The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an outofequilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are however difficult to characterize in experiments at finite drive. Here we show that the correlation functions of the velocity field along the front allow to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient and can be extended to all systems displaying avalanche dynamics.
 1. LPENS (UMR_8023)  Laboratoire de physique de l'ENS  ENS Paris
 2. Champs Aléatoires et Systèmes hors d'Équilibre
 3. DALEMBERT  Institut Jean Le Rond d'Alembert
 4. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 5. IFUFB  Instituto de Fisica, Universidade Federal da Bahia

Universal Survival Probability for a d Dimensional RunandTumble Particle – Archive ouverte HAL
Francesco Mori ^{1} Pierre Le Doussal ^{2} Satya N. Majumdar ^{1} Satya Majumdar ^{1} Gregory Schehr ^{1}
Francesco Mori, Pierre Le Doussal, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Universal Survival Probability for a d Dimensional RunandTumble Particle. Physical Review Letters, American Physical Society, 2020, 124 (9), ⟨10.1103/PhysRevLett.124.090603⟩. ⟨hal02512214⟩
We consider an active runandtumble particle (RTP) in $d$ dimensions and compute exactly the probability $S(t)$ that the $x$component of the position of the RTP does not change sign up to time $t$. When the tumblings occur at a constant rate, we show that $S(t)$ is independent of $d$ for any finite time $t$ (and not just for large $t$), as a consequence of the celebrated Sparre Andersen theorem for discretetime random walks in one dimension. Moreover, we show that this universal result holds for a much wider class of RTP models in which the speed $v$ of the particle after each tumbling is random, drawn from an arbitrary probability distribution. We further demonstrate, as a consequence, the universality of the record statistics in the RTP problem.
 1. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
 2. Champs Aléatoires et Systèmes hors d'Équilibre

Velocity and diffusion constant of an active particle in a onedimensional force field – Archive ouverte HAL
Pierre Le Doussal ^{1} Satya N. Majumdar ^{2} Satya Majumdar ^{2} Gregory Schehr ^{2}
Pierre Le Doussal, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Velocity and diffusion constant of an active particle in a onedimensional force field. EPL  Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2020, 130 (4), pp.40002. ⟨10.1209/02955075/130/40002⟩. ⟨hal02881224⟩
We consider a run an tumble particle with two velocity states $\pm v_0$, in an inhomogeneous force field $f(x)$ in one dimension. We obtain exact formulae for its velocity $V_L$ and diffusion constant $D_L$ for arbitrary periodic $f(x)$ of period $L$. They involve the "active potential" which allows to define a global bias. Upon varying parameters, such as an external force $F$, the dynamics undergoes transitions from nonergodic trapped states, to various moving states, some with non analyticities in the $V_L$ versus $F$ curve. A random landscape in the presence of a bias leads, for large $L$, to anomalous diffusion $x \sim t^\mu$, $\mu<1$, or to a phase with a finite velocity that we calculate.
 1. Champs Aléatoires et Systèmes hors d'Équilibre
 2. LPTMS  Laboratoire de Physique Théorique et Modèles Statistiques
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