arXiv subjects

François Huveneers

Publications and source records attributed to François Huveneers.

At least 19 recordsLinked to original sources

arXiv2026

Mean-Field Convective Phase Separation under Thermal Gradients

Nonequilibrium conditions fundamentally change how systems undergo phase separation. In lattice gases with attractive interactions under temperature gradients, particles have been shown to form periodic patterns and steady convective currents; however, a clear theoretical explanation of this convective phase separation is still missing. Here, we present a dynamical mean-field model that describes the mechanism behind this convective phase separation. Using linear stability analysis, we show that the transition from a uniform state to a periodic pattern is driven by the emergence of a dominant unstable mode. Numerical simulations confirm the predicted phase diagram and demonstrate that these convective currents are a robust feature of the steady state, appearing regardless of the initial conditions. These results provide a direct approach for understanding how temperature gradients drive the formation of steady-state convective patterns.

cond-mat.stat-mech↗

arXiv2025

Long persistence of localization in a disordered anharmonic chain beyond the atomic limit

We establish rigorous bounds on the decorrelation time and thermal transport in the disordered Klein-Gordon chain with a quartic on-site potential, governed by a parameter $λ$. At $λ= 0$, the chain is harmonic, and any form of transport is fully suppressed by Anderson localization. For the anharmonic system, at $λ> 0$, our results show that decorrelation and transport can occur only on time scales that grow faster than any polynomial in $1/λ$ as $λ\to 0$. From a technical perspective, the main novelty of our work is that we don't restrict ourselves to the atomic limit. Instead, we develop perturbation theory around the harmonic system with a fixed harmonic interaction between nearby oscillators. This allows us to compare our mathematical results with previous numerical work and contribute to resolving an ongoing debate, as detailed in a companion paper arXiv:2308.10572.

math-ph↗

arXiv2025

Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds

We study the breakdown of Anderson localization in the one-dimensional nonlinear Klein-Gordon chain, a prototypical example of a disordered classical many-body system. A series of numerical works indicate that an initially localized wave packet spreads polynomially in time, while analytical studies rather suggest a much slower spreading. Here, we focus on the decorrelation time in equilibrium. On the one hand, we provide a mathematical theorem establishing that this time is larger than any inverse power law in the effective anharmonicity parameter $λ$, and on the other hand our numerics show that it follows a power law for a broad range of values of $λ$. This numerical behavior is fully consistent with the power law observed numerically in spreading experiments, and we conclude that the state-of-the-art numerics may well be unable to capture the long-time behavior of such classical disordered systems.

cond-mat.stat-mech↗

arXiv2023

Rigorous and simple results on very slow thermalization, or quasi-localization, of the disordered quantum chain

This paper originates from lectures delivered at the summer school "Fundamental Problems in Statistical Physics XV" in Bruneck, Italy, in 2021. We give a brief and limited introduction into ergodicity-breaking induced by disorder. As the title suggests, we include a simple yet rigorous and original result: For a strongly disordered quantum chain, we exhibit a full set of quasi-local quantities whose dynamics is negligible up to times of order $\exp\{ c (\log W)^{2-ε}\}$, with $ε< 1$, $c$ a numerical constant, and $W$ the disorder strength. Such a result, that is often referred to as "quasi-localization", can in principle be obtained in other systems as well, but for a disordered quantum chain, its proof is relatively short and transparent.

math-ph↗

arXiv2022

Derivation of Euler equations from quantum and classical microscopic dynamics

We derive Euler equations from a Hamiltonian microscopic dynamics. The microscopic system is a one-dimensional disordered harmonic chain, and the dynamics is either quantum or classical. This chain is an Anderson insulator with a symmetry protected mode: Thermal fluctuations are frozen while the low modes ensure the transport of elongation, momentum and mechanical energy, that evolve according to Euler equations in an hyperbolic scaling limit. In this paper, we strengthen considerably our previous results, where we established a limit in mean starting from a local Gibbs state: We now control the second moment of the fluctuations around the average, yielding a limit in probability, and we enlarge the class of admissible initial states.

math-ph↗

arXiv2020

Evolution of a passive particle in a one-dimensional diffusive environment

We study the behavior of a tracer particle driven by a one-dimensional fluctuating potential, defined initially as a Brownian motion, and evolving in time according to the heat equation. We obtain two main results. First, in the short time limit, we show that the fluctuations of the particle become Gaussian and sub-diffusive, with dynamical exponent $3/4$. Second, in the long time limit, we show that the particle is trapped by the local minima of the potential and evolves diffusively i.e. with exponent $1/2$.

math.PR↗

arXiv2020

Pre-thermalization in a classical phonon field: slow relaxation of the number of phonons

We investigate the emergence of an astonishingly long pre-thermal plateau in a classical phonon field, here a harmonic chain with on-site pinning. Integrability is broken by a weak anharmonic on-site potential with strength $λ$. In the small $λ$ limit, the approach to equilibrium of a translation invariant initial state is described by kinetic theory. However, when the phonon band becomes narrow, we find that the (non-conserved) number of phonons relaxes on much longer time scales than kinetic. We establish rigorous bounds on the relaxation time, and develop a theory that yields exact predictions for the dissipation rate in the limit $λ\to 0$. We compare the theoretical predictions with data from molecular dynamics simulations and find good agreement. Our work shows how classical systems may exhibit phenomena which at the first glance appear to require quantization.

cond-mat.stat-mech↗

arXiv2019

Glassy dynamics in strongly anharmonic chains of oscillators

We review the mechanism for transport in strongly anharmonic chains of oscillators near the atomic limit where all oscillators are decoupled. In this regime, the motion of most oscillators remains close to integrable, i.e. quasi-periodic, on very long time scales, while a few chaotic spots move very slowly and redistribute the energy across the system. The material acquires several characteristic properties of dynamical glasses: intermittency, jamming and a drastic reduction of the mobility as a function of the thermodynamical parameters. We consider both classical and quantum systems, though with more emphasis on the former, and we discuss also the connections with quenched disordered systems, which display a similar physics to a large extent.

cond-mat.stat-mech↗

arXiv2019

Equivalence of ensembles, condensation and glassy dynamics in the Bose-Hubbard Hamiltonian

We study mathematically the equilibrium properties of the Bose-Hubbard Hamiltonian in the limit of a vanishing hopping amplitude. This system conserves the energy and the number of particles. We establish the equivalence between the microcanonical and the grand-canonical ensembles for all allowed values of the density of particles $ρ$ and density of energy $\varepsilon$. Moreover, given $ρ$, we show that the system undergoes a transition as $\varepsilon$ increases, from a usual positive temperature state to the infinite temperature state where a macroscopic excess of energy condensates on a single site. Analogous results have been obtained by S. Chatterjee (2017) for a closely related model. We introduce here a different method to tackle this problem, hoping that it reflects more directly the basic understanding stemming from statistical mechanics. We discuss also how, and in which sense, the condensation of energy leads to a glassy dynamics.

cond-mat.stat-mech↗

arXiv2019

Hydrodynamic limit for a disordered harmonic chain

We consider a one-dimensional unpinned chain of harmonic oscillators with random masses. We prove that after hyperbolic scaling of space and time the distributions of the elongation, momentum and energy converge to the solution of the Euler equations. Anderson localization decouples the mechanical modes from the thermal modes, allowing the closure of the energy conservation equation even out of thermal equilibrium. This example shows that the derivation of Euler equations rests primarily on scales separation and not on ergodicity. Furthermore, it follows from our proof that the temperature profile does not evolve in any space-time scale.

math.PR↗

arXiv2018

Many-body delocalization as a quantum avalanche

We propose a multi-scale diagonalization scheme to study disordered one-dimensional chains, in particular the transition between many-body localization (MBL) and the ergodic phase, expected to be governed by resonant spots. Our scheme focuses on the dichotomy MBL versus {ETH} (eigenstate thermalization hypothesis). We show that a few natural assumptions imply that the system is localized with probability one at criticality. On the ergodic side, delocalization is induced by a quantum avalanche seeded by large ergodic spots, whose size diverges at the transition. On the MBL side, the typical localization length tends to a finite universal value at the transition, but there is a divergent length scale related to the response to an inclusion of large ergodic spots. A mean field approximation analytically illustrates these results and predicts as a power-law distribution for thermal inclusions at criticality.

cond-mat.dis-nn↗

arXiv2018

Response to a small external force and fluctuations of a passive particle in a one-dimensional diffusive environment

We investigate the long time behavior of a passive particle evolving in a one-dimensional diffusive random environment, with diffusion constant $D$. We consider two cases: (a) The particle is pulled forward by a small external constant force, and (b) there is no systematic bias. Theoretical arguments and numerical simulations provide evidence that the particle is eventually trapped by the environment. This is diagnosed in two ways: The asymptotic speed of the particle scales quadratically with the external force as it goes to zero, and the fluctuations scale diffusively in the unbiased environment, up to possible logarithmic corrections in both cases. Moreover, in the large $D$ limit (homogenized regime), we find an important transient region giving rise to other, finite-size scalings, and we describe the cross-over to the true asymptotic behavior.

cond-mat.stat-mech↗

arXiv2017

How a small quantum bath can thermalize long localized chains

We investigate the stability of the many-body localized (MBL) phase for a system in contact with a single ergodic grain, modelling a Griffiths region with low disorder. Our numerical analysis provides evidence that even a small ergodic grain consisting of only 3 qubits can delocalize a localized chain, as soon as the localization length exceeds a critical value separating localized and extended regimes of the whole system. We present a simple theory, consistent with the arguments in [Phys. Rev. B 95, 155129 (2017)], that assumes a system to be locally ergodic unless the local relaxation time, determined by Fermi's Golden Rule, is larger than the inverse level spacing. This theory predicts a critical value for the localization length that is perfectly consistent with our numerical calculations. We analyze in detail the behavior of local operators inside and outside the ergodic grain, and find excellent agreement of numerics and theory.

cond-mat.str-el↗

arXiv2017

Classical and quantum systems: transport due to rare events

We review possible mechanisms for energy transfer based on 'rare' or 'non-perturbative' effects, in physical systems that present a many-body localized phenomenology. The main focus is on classical systems, with or without quenched disorder. For non-quantum systems, the breakdown of localization is usually not regarded as an issue, and we thus aim at identifying the fastest channels for transport. Next, we contemplate the possibility of applying the same mechanisms in quantum systems, including disorder free systems (e.g. Bose-Hubbard chain), disordered many-body localized systems with mobility edges at energies below the edge, and strongly disordered lattice systems in $d>1$. For quantum mechanical systems, the relevance of these considerations for transport is currently a matter of debate.

cond-mat.dis-nn↗

arXiv2016

Stability and instability towards delocalization in MBL systems

We propose a theory that describes quantitatively the (in)stability of fully MBL systems due to ergodic, i.e. delocalized, grains, that can be for example due to disorder fluctuations. The theory is based on the ETH hypothesis and elementary notions of perturbation theory. The main idea is that we assume as much chaoticity as is consistent with conservation laws. The theory describes correctly -even without relying on the theory of local integrals of motion (LIOM)- the MBL phase in 1 dimension at strong disorder. It yields an explicit and quantitative picture of the spatial boundary between localized and ergodic systems. We provide numerical evidence for this picture. When the theory is taken to its extreme logical consequences, it predicts that the MBL phase is destabilised in the long time limit whenever 1) interactions decay slower than exponentially in $d=1$ and 2) always in $d>1$. Finer numerics is required to assess these predictions.

cond-mat.dis-nn↗

arXiv2016

Anderson Localisation for periodically driven systems

We study the persistence of localization for a strongly disordered tight-binding Anderson model on the lattice $\mathbb{Z}^d$, periodically driven on each site. Under two different sets of conditions, we show that Anderson localization survives if the driving frequency is higher than some threshold value that we determine. We discuss the implication of our results for recent development in condensed matter physics, we compare them with the predictions issuing from adiabatic theory, and we comment on the connexion with Mott's law, derived within the linear response formalism.

math-ph↗

arXiv2015

Random walk driven by the simple exclusion process

We prove a strong law of large numbers and an annealed invariance principle for a random walk in a one-dimensional dynamic random environment evolving as the simple exclusion process with jump parameter $γ$. First, we establish that if the asymptotic velocity of the walker is non-zero in the limiting case "$γ= \infty$", where the environment gets fully refreshed between each step of the walker, then, for $γ$ large enough, the walker still has a non-zero asymptotic velocity in the same direction. Second, we establish that if the walker is transient in the limiting case $γ= 0$, then, for $γ$ small enough but positive, the walker has a non-zero asymptotic velocity in the direction of the transience. These two limiting velocities can sometimes be of opposite sign. In all cases, we show that the fluctuations are normal.

math.PR↗

arXiv2015

A theory of many-body localization in periodically driven systems

We present a theory of periodically driven, many-body localized (MBL) systems. We argue that MBL persists under periodic driving at high enough driving frequency: The Floquet operator (evolution operator over one driving period) can be represented as an exponential of an effective time-independent Hamiltonian, which is a sum of quasi-local terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the time-dependence from the original Hamiltonian. When the driving evolves smoothly in time, the theory can be sharpened by estimating the probability of adiabatic Landau-Zener transitions at many-body level crossings. In all cases, we argue that there is delocalization at sufficiently low frequency. We propose a phase diagram of driven MBL systems.

cond-mat.dis-nn↗