# Les 20 dernières publications du LPTMS

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## Archive ouverte HAL – Critical Jammed Phase of the Linear Perceptron

### Silvio Franz

^{1}Antonio Sclocchi^{1}Pierfrancesco Urbani^{2}#### Silvio Franz, Antonio Sclocchi, Pierfrancesco Urbani. Critical Jammed Phase of the Linear Perceptron.

*Physical Review Letters*, American Physical Society, 2019, 123 (11), ⟨10.1103/PhysRevLett.123.115702⟩. ⟨hal-02292061⟩Criticality in statistical physics naturally emerges at isolated points in the phase diagram. Jamming of spheres is not an exception: varying density, it is the critical point that separates the unjammed phase where spheres do not overlap and the jammed phase where they cannot be arranged without overlaps. The same remains true in more general constraint satisfaction problems with continuous variables (CCSP) where jamming coincides with the (protocol dependent) satisfiability transition point. In this work we show that by carefully choosing the cost function to be minimized, the region of criticality extends to occupy a whole region of the jammed phase. As a working example, we consider the spherical perceptron with a linear cost function in the unsatisfiable (UNSAT) jammed phase and we perform numerical simulations which show critical power laws emerging in the configurations obtained minimizing the linear cost function. We develop a scaling theory to compute the emerging critical exponents.

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

## Archive ouverte HAL – A super-resolution platform for correlative live single-molecule imaging and STED microscopy

### V. InavalliMartin Lenz

^{1}Corey Butler^{2}Julie Angibaud^{3}Benjamin Compans^{4}Florian Levet^{5}Jan TønnesenOlivier Rossier^{2}Gregory Giannone^{2}Olivier Thoumine^{6}Eric Hosy^{2}Daniel Choquet^{6}Jean-Baptiste Sibarita^{2}U. Valentin Nägerl^{2}#### V. Inavalli, Martin Lenz, Corey Butler, Julie Angibaud, Benjamin Compans, et al.. A super-resolution platform for correlative live single-molecule imaging and STED microscopy.

*Nature Methods*, Nature Publishing Group, 2019, ⟨10.1038/s41592-019-0611-8⟩. ⟨hal-02348164⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. IINS - Interdisciplinary Institute for Neuroscience
- 3. U1064 Inserm - CRTI - Centre de Recherche en Transplantation et Immunologie
- 4. Interdisciplinary Institute for Neuroscience
- 5. LaBRI - Laboratoire Bordelais de Recherche en Informatique
- 6. PCS - Physiologie cellulaire de la synapse

## Archive ouverte HAL – Harmonically Confined Particles with Long-Range Repulsive Interactions

### Sanaa AgarwalAbhishek Dhar

^{1}Manas KulkarniAnupam Kundu^{1}Satya N. Majumdar^{2}David Mukamel^{3}Gregory Schehr^{2}S. n. Majumdar#### Sanaa Agarwal, Abhishek Dhar, Manas Kulkarni, Anupam Kundu, Satya N. Majumdar, et al.. Harmonically Confined Particles with Long-Range Repulsive Interactions.

*Physical Review Letters*, American Physical Society, 2019, 123 (10), ⟨10.1103/PhysRevLett.123.100603⟩. ⟨hal-02295905⟩We study an interacting system of $N$ classical particles on a line at thermal equilibrium. The particles are confined by a harmonic trap and repelling each other via pairwise interaction potential that behaves as a power law $\propto \sum_{\substack{i\neq j}}^N|x_i-x_j|^{-k}$ (with $k>-2$) of their mutual distance. This is a generalization of the well known cases of the one component plasma ($k=-1$), Dyson's log-gas ($k\to 0^+$), and the Calogero-Moser model ($k=2$). Due to the competition between harmonic confinement and pairwise repulsion, the particles spread over a finite region of space for all $k>-2$. We compute exactly the average density profile for large $N$ for all $k>-2$ and show that while it is independent of temperature for sufficiently low temperature, it has a rich and nontrivial dependence on $k$ with distinct behavior for $-2

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

## Archive ouverte HAL – Wave breaking and formation of dispersive shock waves in a defocusing nonlinear optical material

### M. Isoard

^{1}A. M. Kamchatnov^{2}N. Pavloff^{1}#### M. Isoard, A. M. Kamchatnov, N. Pavloff. Wave breaking and formation of dispersive shock waves in a defocusing nonlinear optical material.

*Physical Review A*, American Physical Society 2019, 99 (5), ⟨10.1103/PhysRevA.99.053819⟩. ⟨hal-02291908⟩We theoretically describe the quasi one-dimensional transverse spreading of a light pulse propagating in a nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the pulse can be described within a nondispersive approximation by means of Riemann's approach. For larger distances, wave breaking occurs, leading to the formation of dispersive shocks at both ends of the pulse. We describe this phenomenon within Whitham modulation theory, which yields an excellent agreement with numerical simulations. Our analytic approach makes it possible to extract the leading asymptotic behavior of the parameters of the shock.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Institute of Spectroscopy

## Archive ouverte HAL – The algebraic area of closed lattice random walks

### Stephane Ouvry

^{1}Shuang Wu^{1}#### Stephane Ouvry, Shuang Wu. The algebraic area of closed lattice random walks.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2019, ⟨10.04098⟩. ⟨hal-02292208⟩We propose a formula for the enumeration of closed lattice random walks of length $n$ enclosing a given algebraic area. The information is contained in the Kreft coefficients which encode, in the commensurate case, the Hofstadter secular equation for a quantum particle hopping on a lattice coupled to a perpendicular magnetic field. The algebraic area enumeration is possible because it is split in $2^{n/2-1}$ pieces, each tractable in terms of explicit combinatorial expressions.

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

## Archive ouverte HAL – Gap statistics close to the quantile of a random walk

### Bertrand Lacroix-A-Chez-Toine

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}Satya Majumdar^{1}#### Bertrand Lacroix-A-Chez-Toine, Satya N. Majumdar, Gregory Schehr, Satya Majumdar. Gap statistics close to the quantile of a random walk.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2019, 52 (31), pp.315003. ⟨10.1088/1751-8121/ab2cf9⟩. ⟨hal-02291855⟩We consider a random walk of $n$ steps starting at $x_0=0$ with a double exponential (Laplace) jump distribution. We compute exactly the distribution $p_{k,n}(\Delta)$ of the gap $d_{k,n}$ between the $k^{\rm th}$ and $(k+1)^{\rm th}$ maxima in the limit of large $n$ and large $k$, with $\alpha=k/n$ fixed. We show that the typical fluctuations of the gaps, which are of order $O( n^{-1/2})$, are described by a universal $\alpha$-dependent distribution, which we compute explicitly. Interestingly, this distribution has an inverse cubic tail, which implies a non-trivial $n$-dependence of the moments of the gaps. We also argue, based on numerical simulations, that this distribution is universal, i.e. it holds for more general jump distributions (not only the Laplace distribution), which are continuous, symmetric with a well defined second moment. Finally, we also compute the large deviation form of the gap distribution $p_{\alpha n,n}(\Delta)$ for $\Delta=O(1)$, which turns out to be non-universal.

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

## Archive ouverte HAL – Distribution of Brownian coincidences

### Alexandre Krajenbrink

^{1}Bertrand Lacroix-A-Chez-Toine^{2}Pierre Le Doussal^{3}#### Alexandre Krajenbrink, Bertrand Lacroix-A-Chez-Toine, Pierre Le Doussal. Distribution of Brownian coincidences.

*Journal of Statistical Physics*, Springer Verlag, 2019. ⟨hal-02295902⟩We study the probability distribution, $P_N(T)$, of the coincidence time $T$, i.e. the total local time of all pairwise coincidences of $N$ independent Brownian walkers. We consider in details two geometries: Brownian motions all starting from $0$, and Brownian bridges. Using a Feynman-Kac representation for the moment generating function of this coincidence time, we map this problem onto some observables in three related models (i) the propagator of the Lieb Liniger model of quantum particles with pairwise delta function interactions (ii) the moments of the partition function of a directed polymer in a random medium (iii) the exponential moments of the solution of the Kardar-Parisi-Zhang equation. Using these mappings, we obtain closed formulae for the probability distribution of the coincidence time, its tails and some of its moments. Its asymptotics at large and small coincidence time are also obtained for arbitrary fixed endpoints. The universal large $T$ tail, $P_N(T) \sim \exp(- 3 T^2/(N^3-N))$ is obtained, and is independent of the geometry. We investigate the large deviations in the limit of a large number of walkers through a Coulomb gas approach. Some of our analytical results are compared with numerical simulations.

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

## Archive ouverte HAL – Lattice Boltzmann Electrokinetics simulation of nanocapacitors

### Adelchi J. Asta

^{1}Ivan Palaia^{2}Emmanuel Trizac^{2}Maximilien Levesque^{3}Benjamin Rotenberg^{4}#### Adelchi J. Asta, Ivan Palaia, Emmanuel Trizac, Maximilien Levesque, Benjamin Rotenberg. Lattice Boltzmann Electrokinetics simulation of nanocapacitors.

*Journal of Chemical Physics*, American Institute of Physics, 2019. ⟨hal-02295839⟩We propose a method to model metallic surfaces in Lattice Boltzmann Electrokinetics simulations (LBE), a lattice-based algorithm rooted in kinetic theory which captures the coupled solvent and ion dynamics in electrolyte solutions. This is achieved by a simple rule to impose electrostatic boundary conditions, in a consistent way with the location of the hydrodynamic interface for stick boundary conditions. The proposed method also provides the local charge induced on the electrode by the instantaneous distribution of ions under voltage. We validate it in the low voltage regime by comparison with analytical results in two model nanocapacitors: parallel plate and coaxial electrodes. We examine the steady-state ionic concentrations and electric potential profiles (and corresponding capacitance), the time-dependent response of the charge on the electrodes, as well as the steady-state electro-osmotic profiles in the presence of an additional, tangential electric field. The LBE method further provides the time-dependence of these quantities, as illustrated on the electro-osmotic response. While we do not consider this case in the present work, which focuses on the validation of the method, the latter readily applies to large voltages between the electrodes, as well as to time-dependent voltages. This work opens the way to the LBE simulation of more complex systems involving electrodes and metallic surfaces, such as sensing devices based on nanofluidic channels and nanotubes, or porous electrodes.

- 1. PHENIX - PHysicochimie des Electrolytes et Nanosystèmes InterfaciauX
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. PASTEUR - Processus d'Activation Sélective par Transfert d'Energie Uni-électronique ou Radiatif (UMR 8640)
- 4. PECSA - Physicochimie des Electrolytes, Colloïdes et Sciences Analytiques

## Archive ouverte HAL – On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system

### Maurizio Fagotti

^{1, 2}#### Maurizio Fagotti. On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system.

*SciPost Physics*, SciPost Foundation, 2019, 6 (5), ⟨10.21468/SciPostPhys.6.5.059⟩. ⟨hal-02292090⟩We consider the time evolution of a state in an isolated quantum spin lattice system with energy cumulants proportional to the number of the sites $L^d$. We compute the distribution of the eigenvalues of the time averaged state over a time window $[t_0,t_0+t]$ in the limit of large $L$. This allows us to infer the size of a subspace that captures time evolution in $[t_0,t_0+t]$ with an accuracy $1-\epsilon$. We estimate the size to be $ \frac{\sqrt{2\mathfrak{e}_2}}{\pi}\mathrm{erf}^{-1}(1-\epsilon) L^{\frac{d}{2}}t$, where $\mathfrak{e}_2$ is the energy variance per site, and $\mathrm{erf}^{-1}$ is the inverse error function.

- 1. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Impact of jamming criticality on low-temperature anomalies in structural glasses

### Silvio Franz

^{1}Thibaud Maimbourg^{2, 1}Giorgio Parisi^{3}Antonello Scardicchio^{4}#### Silvio Franz, Thibaud Maimbourg, Giorgio Parisi, Antonello Scardicchio. Impact of jamming criticality on low-temperature anomalies in structural glasses.

*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2019, 116 (28), pp.13768-13773. ⟨10.1073/pnas.1820360116⟩. ⟨hal-02292219⟩We present a novel mechanism for the anomalous behaviour of the specific heat in low-temperature amorphous solids. The analytic solution of a mean-field model belonging to the same universality class as high-dimensional glasses, the spherical perceptron, suggests that there exists a crossover temperature above which the specific heat scales linearly with temperature while below it a cubic scaling is displayed. This relies on two crucial features of the phase diagram: (i) The marginal stability of the free-energy landscape, which induces a gapless phase responsible for the emergence of a power-law scaling (ii) The vicinity of the classical jamming critical point, as the crossover temperature gets lowered when approaching it. This scenario arises from a direct study of the thermodynamics of the system in the quantum regime, where we show that, contrary to crystals, the Debye approximation does not hold.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTENS - Laboratoire de Physique Théorique de l'ENS
- 3. Center for Statistical Mechanics and Complexity, INFM Roma 'La Sapienza' and Dipartimento di Fisica
- 4. ICTP - Abdus Salam International Centre for Theoretical Physics [Trieste]

## Archive ouverte HAL – Noncrossing run-and-tumble particles on a line

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Pierre Le Doussal^{1}Satya Majumdar^{2}Gregory Schehr^{2}#### Pierre Le Doussal, Satya N. Majumdar, Pierre Le Doussal, Satya Majumdar, Gregory Schehr. Noncrossing run-and-tumble particles on a line.

*Physical Review E*, American Physical Society (APS), 2019, 100 (1), ⟨10.1103/PhysRevE.100.012113⟩. ⟨hal-02291902⟩We study active particles performing independent run and tumble motion on an infinite line with velocities $v_0 \sigma(t)$, where $\sigma(t) = \pm 1$ is a dichotomous telegraphic noise with constant flipping rate $\gamma$. We first consider one particle in the presence of an absorbing wall at $x=0$ and calculate the probability that it has survived up to time $t$ and is at position $x$ at time $t$. We then consider two particles with independent telegraphic noises and compute exactly the probability that they do not cross up to time $t$. Contrarily to the case of passive (Brownian) particles this two-RTP problem can not be reduced to a single RTP with an absorbing wall. Nevertheless, we are able to compute exactly the probability of no-crossing of two independent RTP's up to time $t$ and find that it decays at large time as $t^{-1/2}$ with an amplitude that depends on the initial condition. The latter allows to define an effective length scale, analogous to the so called `` Milne extrapolation length'' in neutron scattering, which we demonstrate to be a fingerprint of the active dynamics.

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

## Archive ouverte HAL – Topological proximity effects in a Haldane graphene bilayer system

### Peng Cheng

^{1}Philipp W. KleinKirill Plekhanov^{2, 3}Klaus Sengstock^{4}Monika AidelsburgerChristof Weitenberg^{5}Karyn Le Hur^{2}Philipp KleinKaryn Le Hur^{2}#### Peng Cheng, Philipp W. Klein, Kirill Plekhanov, Klaus Sengstock, Monika Aidelsburger, et al.. Topological proximity effects in a Haldane graphene bilayer system.

*Physical Review B : Condensed matter and materials physics*, American Physical Society, 2019, 100 (8), ⟨10.1103/PhysRevB.100.081107⟩. ⟨hal-02291915⟩We reveal a proximity effect between a topological band (Chern) insulator described by a Haldane model and spin-polarized Dirac particles of a graphene layer. Coupling weakly the two systems through a tunneling term in the bulk, the topological Chern insulator induces a gap and an opposite Chern number on the Dirac particles at half-filling resulting in a sign flip of the Berry curvature at one Dirac point. We study different aspects of the bulk-edge correspondence and present protocols to observe the evolution of the Berry curvature as well as two counter-propagating (protected) edge modes with different velocities. In the strong-coupling limit, the energy spectrum shows flat bands. Therefore we build a perturbation theory and address further the bulk-edge correspondence. We also show the occurrence of a topological insulating phase with Chern number one when only the lowest band is filled. We generalize the effect to Haldane bilayer systems with asymmetric Semenoff masses. We propose an alternative definition of the topological invariant on the Bloch sphere.

- 1. DALEMBERT - Institut Jean Le Rond d'Alembert
- 2. CPHT - Centre de Physique Théorique [Palaiseau]
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Zentrum für Optische Quantentechnologien
- 5. MPQ - Max-Planck-Institut für Quantenoptik

## Archive ouverte HAL – One-dimensional two-component fermions with contact even-wave repulsion and SU(2)-symmetry-breaking near-resonant odd-wave attraction

### D. V. Kurlov

^{1}S. I. Matveenko^{2}V. Gritsev^{3}G. V. Shlyapnikov^{2}#### D. V. Kurlov, S. I. Matveenko, V. Gritsev, G. V. Shlyapnikov. One-dimensional two-component fermions with contact even-wave repulsion and SU(2)-symmetry-breaking near-resonant odd-wave attraction.

*Physical Review A*, American Physical Society 2019, 99 (4), ⟨10.1103/PhysRevA.99.043631⟩. ⟨hal-02291881⟩We consider a one-dimensional (1D) two-component atomic Fermi gas with contact interaction in the even-wave channel (Yang-Gaudin model) and study the effect of an SU(2) symmetry breaking near-resonant odd-wave interaction within one of the components. Starting from the microscopic Hamiltonian, we derive an effective field theory for the spin degrees of freedom using the bosonization technique. It is shown that at a critical value of the odd-wave interaction there is a first-order phase transition from a phase with zero total spin and zero magnetization to the spin-segregated phase where the magnetization locally differs from zero.

- 1. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Physics Department

## Archive ouverte HAL – One-dimensional two-component fermions with contact even-wave repulsion and SU(2)-symmetry-breaking near-resonant odd-wave attraction

### D. V. Kurlov

^{1}S. I. Matveenko^{2}V. Gritsev^{3}G. V. Shlyapnikov^{2}#### D. V. Kurlov, S. I. Matveenko, V. Gritsev, G. V. Shlyapnikov. One-dimensional two-component fermions with contact even-wave repulsion and SU(2)-symmetry-breaking near-resonant odd-wave attraction.

*Physical Review A*, American Physical Society 2019, 99 (4), ⟨10.1103/PhysRevA.99.043631⟩. ⟨hal-02291881⟩We consider a one-dimensional (1D) two-component atomic Fermi gas with contact interaction in the even-wave channel (Yang-Gaudin model) and study the effect of an SU(2) symmetry breaking near-resonant odd-wave interaction within one of the components. Starting from the microscopic Hamiltonian, we derive an effective field theory for the spin degrees of freedom using the bosonization technique. It is shown that at a critical value of the odd-wave interaction there is a first-order phase transition from a phase with zero total spin and zero magnetization to the spin-segregated phase where the magnetization locally differs from zero.

- 1. VAN DER WAALS-ZEEMAN INSTITUTE - University of Amsterdam Van der Waals-Zeeman Institute
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Physics Department

## Archive ouverte HAL – Distribution of Brownian coincidences

### Alexandre Krajenbrink

^{1}Bertrand Lacroix-A-Chez-Toine^{2}Pierre Le Doussal^{3}#### Alexandre Krajenbrink, Bertrand Lacroix-A-Chez-Toine, Pierre Le Doussal. Distribution of Brownian coincidences.

*Journal of Statistical Physics*, Springer Verlag, 2019. ⟨hal-02295902⟩We study the probability distribution, $P_N(T)$, of the coincidence time $T$, i.e. the total local time of all pairwise coincidences of $N$ independent Brownian walkers. We consider in details two geometries: Brownian motions all starting from $0$, and Brownian bridges. Using a Feynman-Kac representation for the moment generating function of this coincidence time, we map this problem onto some observables in three related models (i) the propagator of the Lieb Liniger model of quantum particles with pairwise delta function interactions (ii) the moments of the partition function of a directed polymer in a random medium (iii) the exponential moments of the solution of the Kardar-Parisi-Zhang equation. Using these mappings, we obtain closed formulae for the probability distribution of the coincidence time, its tails and some of its moments. Its asymptotics at large and small coincidence time are also obtained for arbitrary fixed endpoints. The universal large $T$ tail, $P_N(T) \sim \exp(- 3 T^2/(N^3-N))$ is obtained, and is independent of the geometry. We investigate the large deviations in the limit of a large number of walkers through a Coulomb gas approach. Some of our analytical results are compared with numerical simulations.

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

## Archive ouverte HAL – Three-body interaction near a narrow two-body zero crossing

### A. Pricoupenko

^{1}D. S. Petrov^{1}#### A. Pricoupenko, D. S. Petrov. Three-body interaction near a narrow two-body zero crossing.

*Physical Review A*, American Physical Society 2019, 100 (4), ⟨10.1103/PhysRevA.100.042707⟩. ⟨hal-02395504⟩We calculate the effective three-body force for bosons interacting with each other by a two-body potential tuned to a narrow zero crossing in any dimension. We use the standard two-channel model parametrized by the background atom-atom interaction strength, the amplitude of the open-channel to closed-channel coupling, and the atom-dimer interaction strength. The three-body force originates from the atom-dimer interaction, but it can be dramatically enhanced for narrow crossings, i.e., for small atom-dimer conversion amplitudes. This effect can be used to stabilize quasi-two-dimensional dipolar atoms and molecules.

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

## Archive ouverte HAL – Gap statistics close to the quantile of a random walk

### Bertrand Lacroix-A-Chez-Toine

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}Satya Majumdar^{1}#### Bertrand Lacroix-A-Chez-Toine, Satya N. Majumdar, Gregory Schehr, Satya Majumdar. Gap statistics close to the quantile of a random walk.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2019, 52 (31), pp.315003. ⟨10.1088/1751-8121/ab2cf9⟩. ⟨hal-02291855⟩We consider a random walk of $n$ steps starting at $x_0=0$ with a double exponential (Laplace) jump distribution. We compute exactly the distribution $p_{k,n}(\Delta)$ of the gap $d_{k,n}$ between the $k^{\rm th}$ and $(k+1)^{\rm th}$ maxima in the limit of large $n$ and large $k$, with $\alpha=k/n$ fixed. We show that the typical fluctuations of the gaps, which are of order $O( n^{-1/2})$, are described by a universal $\alpha$-dependent distribution, which we compute explicitly. Interestingly, this distribution has an inverse cubic tail, which implies a non-trivial $n$-dependence of the moments of the gaps. We also argue, based on numerical simulations, that this distribution is universal, i.e. it holds for more general jump distributions (not only the Laplace distribution), which are continuous, symmetric with a well defined second moment. Finally, we also compute the large deviation form of the gap distribution $p_{\alpha n,n}(\Delta)$ for $\Delta=O(1)$, which turns out to be non-universal.

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

## Archive ouverte HAL – Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point

### Grégoire Misguich

^{1}Nicolas Pavloff^{2}Vincent Pasquier^{1}#### Grégoire Misguich, Nicolas Pavloff, Vincent Pasquier. Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point.

*SciPost Physics*, SciPost Foundation, 2019, 7 (2), ⟨10.21468/SciPostPhys.7.2.025⟩. ⟨hal-02295825⟩We study the dynamics of a spin-1/2 XXZ chain which is initially prepared in a domain-wall state. We compare the results of time-dependent Density Matrix Renormalization Group simulations with those of an effective description in terms of a classical anisotropic Landau-Lifshitz (LL) equation. Numerous quantities are analyzed: magnetization (x, y and z components), energy density, energy current, but also some spin-spin correlation functions or entanglement entropy in the quantum chain. Without any adjustable parameter a quantitative agreement is observed between the quantum and the LL problems in the long time limit, when the models are close to the isotropic point. This is explained as a consequence of energy conservation. At the isotropic point the mapping between the LL equation and the nonlinear Schr\"odinger equation is used to construct a variational solution capturing several aspects of the problem.

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

## Archive ouverte HAL – Quadratic Mean Field Games

### Denis Ullmo

^{1}Igor Swiecicki^{2, 1}Thierry Gobron^{2}#### Denis Ullmo, Igor Swiecicki, Thierry Gobron. Quadratic Mean Field Games.

*Physics Reports*, Elsevier, 2019. ⟨hal-02291869⟩Mean field games were introduced independently by J-M. Lasry and P-L. Lions, and by M. Huang, R.P. Malham\'e and P. E. Caines, in order to bring a new approach to optimization problems with a large number of interacting agents. The description of such models split in two parts, one describing the evolution of the density of players in some parameter space, the other the value of a cost functional each player tries to minimize for himself, anticipating on the rational behavior of the others. Quadratic Mean Field Games form a particular class among these systems, in which the dynamics of each player is governed by a controlled Langevin equation with an associated cost functional quadratic in the control parameter. In such cases, there exists a deep relationship with the non-linear Schr\"odinger equation in imaginary time, connexion which lead to effective approximation schemes as well as a better understanding of the behavior of Mean Field Games. The aim of this paper is to serve as an introduction to Quadratic Mean Field Games and their connexion with the non-linear Schr\"odinger equation, providing to physicists a good entry point into this new and exciting field.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTM - Laboratoire de Physique Théorique et Modélisation

## Archive ouverte HAL – Enhancement of many-body quantum interference in chaotic bosonic systems

### Peter Schlagheck

^{1}Denis Ullmo^{2}Juan Diego Urbina^{3}Klaus RichterSteven Tomsovic^{4}#### Peter Schlagheck, Denis Ullmo, Juan Diego Urbina, Klaus Richter, Steven Tomsovic. Enhancement of many-body quantum interference in chaotic bosonic systems.

*Physical Review Letters*, American Physical Society, 2019, 123, pp.215302. ⟨10.1103/PhysRevLett.123.215302⟩. ⟨hal-02361335⟩Although highly successful, the truncated Wigner approximation (TWA) leaves out many-body quantum interference between mean-field Gross-Pitaevskii solutions as well as other quantum effects, and is therefore essentially classical. Turned around, this implies that if a system's quantum properties deviate from TWA, they must be exhibiting some quantum phenomenon, such as localization, diffraction, or tunneling. Here, we consider in detail a particular interference effect arising from discrete symmetries, which can lead to a significant enhancement of quantum observables with respect to the TWA prediction, and derive an augmented version of the TWA in order to incorporate them. Using the Bose-Hubbard model for illustration, we further show strong evidence for the presence of dynamical localization due to remaining differences between the TWA predictions and quantum results.

- 1. Institut für Theoretische Physik
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. UR - Universität Regensburg
- 4. Department of Physics