# Les 20 dernières publications du LPTMS

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## Archive ouverte HAL – Fluctuation-dominated phase ordering at a mixed order transition

### Mustansir Barma

^{1}Satya N. Majumdar^{2}David Mukamel^{3}Satya Majumdar^{2}#### Mustansir Barma, Satya N. Majumdar, David Mukamel, Satya Majumdar. Fluctuation-dominated phase ordering at a mixed order transition.

*Journal of Physics A: Mathematical and Theoretical*, IOP Publishing, 2019, 52 (25), pp.254001. ⟨10.1088/1751-8121/ab2064⟩. ⟨hal-02291900⟩Mixed order transitions are those which show a discontinuity of the order parameter as well as a divergent correlation length. We show that the behaviour of the order parameter correlation function along the transition line of mixed order transitions can change from normal critical behaviour with power law decay, to fluctuation-dominated phase ordering as a parameter is varied. The defining features of fluctuation-dominated order are anomalous fluctuations which remain large in the thermodynamic limit, and correlation functions which approach a finite value through a cusp singularity as the separation scaled by the system size approaches zero. We demonstrate that fluctuation-dominated order sets in along a portion of the transition line of an Ising model with truncated long-range interactions which was earlier shown to exhibit mixed order transitions, and also argue that this connection should hold more generally.

- 1. Department of Theoretical Physics
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Weizmann Institute

## 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

## Archive ouverte HAL – Correlated Rigidity Percolation and Colloidal Gels

### Shang ZhangLeyou ZhangMehdi Bouzid

^{1, 2}D. Zeb RocklinEmanuela del Gado^{3}Xiaoming Mao^{4}#### Shang Zhang, Leyou Zhang, Mehdi Bouzid, D. Zeb Rocklin, Emanuela del Gado, et al.. Correlated Rigidity Percolation and Colloidal Gels.

*Physical Review Letters*, American Physical Society, 2019, 123 (5), ⟨10.1103/PhysRevLett.123.058001⟩. ⟨hal-02291872⟩Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid transitions, such as colloidal gelation, which are due to attractive interactions and aggregation. Using a lattice model, we show that structural correlations shift RP to lower volume fractions. Through molecular dynamics simulations, we show that increasing attraction in colloidal gelation increases structural correlation and thus lowers the RP transition, agreeing with experiments. Hence colloidal gelation can be understood as a RP transition, but occurs at volume fractions far below values predicted by the classical RP, due to attractive interactions which induce structural correlation.

- 1. PMMH - Physique et mécanique des milieux hétérogenes
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. LCVN - Laboratoire des colloïdes, verres et nanomatériaux
- 4. UIUC - Physics Department

## Archive ouverte HAL – Tunable corrugated patterns in an active nematic sheet

### Anis Senoussi

^{1}Shunnichi Kashida^{1}Raphaël Voituriez^{2}Jean-Christophe Galas^{1}Ananyo Maitra^{3}André Estévez-Torres^{1}#### Anis Senoussi, Shunnichi Kashida, Raphaël Voituriez, Jean-Christophe Galas, Ananyo Maitra, et al.. Tunable corrugated patterns in an active nematic sheet.

*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2019, pp.201912223. ⟨10.1073/pnas.1912223116⟩. ⟨hal-02334253⟩- 1. LJP - Laboratoire Jean Perrin
- 2. LJP - Laboratoire Jean Perrin
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – New analysis of the free energy cost of interfaces in spin glasses

### Valerio Astuti

^{1}Silvio Franz^{2}Giorgio Parisi^{3}#### Valerio Astuti, Silvio Franz, Giorgio Parisi. New analysis of the free energy cost of interfaces in spin glasses.

*Journal of Physics A: Mathematical and General*, IOP Publishing, 2019, ⟨10.13013⟩. ⟨hal-02291847⟩In this work we want to enhance the calculation performed by Franz, Parisi and Virasoro (FPV) to estimate the free energy cost of interfaces in spin glasses and evaluate the lower critical dimension at which replica symmetry is restored. In particular we evaluate the free energy cost for a general class of effective Hamiltonians showing full replica symmetry breaking, and study the dependence of this cost on the order parameter and on the temperature. We confirm the findings of the FPV papers for the scaling of the free energy, recovering a value for the lower critical dimension of $D_{lc} = 2.5$. In addition to their results we find a non-trivial dependence of the free energy density cost on the order parameter and the temperature. Apart from the case of a restricted class of effective Hamiltonians this dependence cannot be expressed in terms of functions with a clear physical interpretation, as is the case in hierarchical models. In addition we connect the results on the lower critical dimension with recent simulations.

- 1. Dipartimento di Fisica, Università “La Sapienza"
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Center for Statistical Mechanics and Complexity, INFM Roma 'La Sapienza' and Dipartimento di Fisica

## Archive ouverte HAL – Poincaré invariance in NRQCD and potential NRQCD revisited

### Matthias BerweinNora Brambilla

^{1}Sungmin Hwang^{2}Antonio Vairo^{1}#### Matthias Berwein, Nora Brambilla, Sungmin Hwang, Antonio Vairo. Poincaré invariance in NRQCD and potential NRQCD revisited.

*Physical Review D*, American Physical Society, 2019, 99 (9), ⟨10.1103/PhysRevD.99.094008⟩. ⟨hal-02292167⟩We investigate how fields transform under the Poincar\'e group in nonrelativistic effective field theories of QCD. In constructing these transformations, we rely only on symmetries and field redefinitions to limit the number of allowed terms. By requiring invariance of the action under these transformations, nontrivial relations between Wilson coefficients for both nonrelativistic QCD and potential nonrelativistic QCD are derived. We show explicitly how the Poincar\'e algebra is satisfied, and how this gives complementary information on the Wilson coefficients. We also briefly discuss the implications of our results, as well as the possibility of applying this method to other types of effective field theories.

- 1. Physik Department [Garching]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – The equilibrium landscape of the Heisenberg spin chain

### Enej IlievskiEoin Quinn

^{1}#### Enej Ilievski, Eoin Quinn. The equilibrium landscape of the Heisenberg spin chain.

*SciPost Physics*, SciPost Foundation, 2019, 7 (3), ⟨10.21468/SciPostPhys.7.3.033⟩. ⟨hal-02295879⟩We characterise the equilibrium landscape, the entire manifold of local equilibrium states, of an interacting integrable quantum model. Focusing on the isotropic Heisenberg spin chain, we describe in full generality two complementary frameworks for addressing equilibrium ensembles: the functional integral Thermodynamic Bethe Ansatz approach, and the lattice regularisation transfer matrix approach. We demonstrate the equivalence between the two, and in doing so clarify several subtle features of generic equilibrium states. In particular we explain the breakdown of the canonical Y-system, which reflects a hidden structure in the parametrisation of equilibrium ensembles.

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

## Archive ouverte HAL – Correlated Rigidity Percolation and Colloidal Gels

### Shang ZhangLeyou ZhangMehdi Bouzid

^{1, 2}D. Zeb RocklinEmanuela del Gado^{3}Xiaoming Mao^{4}#### Shang Zhang, Leyou Zhang, Mehdi Bouzid, D. Zeb Rocklin, Emanuela del Gado, et al.. Correlated Rigidity Percolation and Colloidal Gels.

*Physical Review Letters*, American Physical Society, 2019, 123 (5), ⟨10.1103/PhysRevLett.123.058001⟩. ⟨hal-02291872⟩Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid transitions, such as colloidal gelation, which are due to attractive interactions and aggregation. Using a lattice model, we show that structural correlations shift RP to lower volume fractions. Through molecular dynamics simulations, we show that increasing attraction in colloidal gelation increases structural correlation and thus lowers the RP transition, agreeing with experiments. Hence colloidal gelation can be understood as a RP transition, but occurs at volume fractions far below values predicted by the classical RP, due to attractive interactions which induce structural correlation.

- 1. PMMH - Physique et mécanique des milieux hétérogenes
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. LCVN - Laboratoire des colloïdes, verres et nanomatériaux
- 4. UIUC - 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 – 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 – One-Dimensional Quasicrystals with Power-Law Hopping

### X. DengS. RayS. Sinha

^{1}G. v. Shlyapnikov^{2}L. Santos#### X. Deng, S. Ray, S. Sinha, G. v. Shlyapnikov, L. Santos. One-Dimensional Quasicrystals with Power-Law Hopping.

*Physical Review Letters*, American Physical Society, 2019, 123 (2), ⟨10.1103/PhysRevLett.123.025301⟩. ⟨hal-02291885⟩One-dimensional quasi-periodic systems with power-law hopping, $1/r^a$, differ from both the standard Aubry-Azbel-Harper (AAH) model and from power-law systems with uncorrelated disorder. Whereas in the AAH model all single-particle states undergo a transition from ergodic to localized at a critical quasi-disorder strength, short-range power-law hops with $a>1$ can result in mobility edges. Interestingly, there is no localization for long-range hops with $a\leq 1$, in contrast to the case of uncorrelated disorder. Systems with long-range hops are rather characterized by ergodic-to-multifractal edges and a phase transition from ergodic to multifractal (extended but non ergodic) states. We show that both mobility and ergodic-to-multifractal edges may be clearly revealed in experiments on expansion dynamics.

- 1. TU/e - Eindhoven University of Technology [Eindhoven]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Far-from-equilibrium noise-heating and laser-cooling dynamics in radio-frequency Paul traps

### A. Maitra

^{1}D. Leibfried^{2}D. Ullmo^{1}H. Landa^{1}#### A. Maitra, D. Leibfried, D. Ullmo, H. Landa. Far-from-equilibrium noise-heating and laser-cooling dynamics in radio-frequency Paul traps.

*Physical Review A*, American Physical Society 2019, 99 (4), ⟨10.1103/PhysRevA.99.043421⟩. ⟨hal-02291892⟩We study the stochastic dynamics of a particle in a periodically driven potential. For atomic ions trapped in radio-frequency Paul traps, noise heating and laser cooling typically act slowly in comparison with the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, which would otherwise be conserved within the regular regions of the Hamiltonian phase space. We present a semiclassical theory of low-saturation laser cooling applicable from the limit of low-amplitude motion to large-amplitude motion, accounting fully for the time-dependent and anharmonic trap. We employ our approach to a detailed study of the stochastic dynamics of a single ion, drawing general conclusions regarding the nonequilibrium dynamics of laser-cooled trapped ions. We predict a regime of anharmonic motion in which laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as it is to heat it), and can also turn into effective heating. This implies that a high-energy ion could be easily lost from the trap despite being laser cooled; however, we find that this loss can be counteracted using a laser detuning much larger than Doppler detuning.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. NIST - National Institute of Standards and Technology [Gaithersburg]

## 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 – 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 – Can a periodically driven particle resist laser cooling and noise?

### A. Maitra

^{1}D. Leibfried^{2}D. Ullmo^{1}H. Landa^{1}#### A. Maitra, D. Leibfried, D. Ullmo, H. Landa. Can a periodically driven particle resist laser cooling and noise?.

*Physical Review Research*, American Physical Society, 2019, ⟨10.01856⟩. ⟨hal-02395528⟩Studying a single atomic ion confined in a time-dependent periodic anharmonic potential, we find large amplitude trajectories stable for millions of oscillation periods in the presence of stochastic laser cooling. The competition between energy gain from the time-dependent drive and damping leads to the stabilization of such stochastic limit cycles. Instead of converging to the global minimum of the averaged potential, the steady-state phase-space distribution develops multiple peaks in the regions of phase space where the frequency of the motion is close to a multiple of the periodic drive. Such distinct nonequilibrium behaviour can be observed in realistic radio-frequency traps with laser-cooled ions, suggesting that Paul traps offer a well-controlled test-bed for studying transport and dynamics of microscopically driven systems.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. NIST - National Institute of Standards and Technology [Gaithersburg]

## Archive ouverte HAL – One-Dimensional Quasicrystals with Power-Law Hopping

### X. DengS. RayS. Sinha

^{1}G. v. Shlyapnikov^{2}L. Santos#### X. Deng, S. Ray, S. Sinha, G. v. Shlyapnikov, L. Santos. One-Dimensional Quasicrystals with Power-Law Hopping.

*Physical Review Letters*, American Physical Society, 2019, 123 (2), ⟨10.1103/PhysRevLett.123.025301⟩. ⟨hal-02291885⟩One-dimensional quasi-periodic systems with power-law hopping, $1/r^a$, differ from both the standard Aubry-Azbel-Harper (AAH) model and from power-law systems with uncorrelated disorder. Whereas in the AAH model all single-particle states undergo a transition from ergodic to localized at a critical quasi-disorder strength, short-range power-law hops with $a>1$ can result in mobility edges. Interestingly, there is no localization for long-range hops with $a\leq 1$, in contrast to the case of uncorrelated disorder. Systems with long-range hops are rather characterized by ergodic-to-multifractal edges and a phase transition from ergodic to multifractal (extended but non ergodic) states. We show that both mobility and ergodic-to-multifractal edges may be clearly revealed in experiments on expansion dynamics.

- 1. TU/e - Eindhoven University of Technology [Eindhoven]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## 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 – Anderson-like localization transition of random walks with resetting

### Denis Boyer

^{1}Andrea Falcón-Cortés^{2}Luca Giuggioli^{3}Satya N. Majumdar^{4}Satya Majumdar^{4}#### Denis Boyer, Andrea Falcón-Cortés, Luca Giuggioli, Satya N. Majumdar, Satya Majumdar. Anderson-like localization transition of random walks with resetting.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2019, 2019 (5), pp.053204. ⟨10.1088/1742-5468/ab16c2⟩. ⟨hal-02291906⟩We study several lattice random walk models with stochastic resetting to previously visited sites which exhibit a phase transition between an anomalous diffusive regime and a localization regime where diffusion is suppressed. The localized phase settles above a critical resetting rate, or rate of memory use, and the probability density asymptotically adopts in this regime a non-equilibrium steady state similar to that of the well known problem of diffusion with resetting to the origin. The transition occurs because of the presence of a single impurity site where the resetting rate is lower than on other sites, and around which the walker spontaneously localizes. Near criticality, the localization length diverges with a critical exponent that falls in the same class as the self-consistent theory of Anderson localization of waves in random media. The critical dimensions are also the same in both problems. Our study provides analytically tractable examples of localization transitions in path-dependent, reinforced stochastic processes, which can be also useful for understanding spatial learning by living organisms.

- 1. Instituto de Fisica
- 2. UNAM - Universidad Nacional Autónoma de México
- 3. University of Bristol [Bristol]
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – How collective asperity detachments nucleate slip at frictional interfaces

### Tom W. J. de GeusMarko Popović

^{1}Wencheng JiAlberto Rosso^{2}Matthieu Wyart^{3}#### Tom W. J. de Geus, Marko Popović, Wencheng Ji, Alberto Rosso, Matthieu Wyart. How collective asperity detachments nucleate slip at frictional interfaces.

*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2019. ⟨hal-02395574⟩Sliding at a quasi-statically loaded frictional interface occurs via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a novel microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius $A_c$ governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding $x_\sigma$ presents a pseudo-gap $P(x_\sigma) \sim (x_\sigma)^\theta$, where $\theta$ is a non-universal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudo-gap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite size effect, while the slip nucleation radius $A_c$ diverges as a $\theta$-dependent power law of the system size. We discuss how these predictions can be tested experimentally.

- 1. MPI-PKS - Max Planck Institute for the Physics of Complex Systems
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. EPFL - Ecole Polytechnique Fédérale de Lausanne

## 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