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Francois Huveneers

Publications and source records attributed to Francois Huveneers.

9 recordsLinked to original sources
arXiv2025

Convection Patterns in Nonequilibrium Kawasaki Dynamics at Low Temperature

We study a conservative stochastic lattice gas (Kawasaki dynamics) coupled in the bulk to a heat bath, which leads to standard phase separation at low uniform temperatures. Instead, a macroscopic temperature gradient drives the system into a nonequilibrium steady state. In this state, the usual long-range order is replaced by robust convection patterns, featuring regularly spaced stripe structures. We show that these nonequilibrium states differ markedly from equilibrium configurations with the same local temperature profiles. Finally, we develop a macroscopic description that captures these behaviors and provides a unified framework for understanding the observed patterns.

cond-mat.stat-mech↗
arXiv2025

Sub-Power Law Decay of the Wave Packet Maximum in Disordered Anharmonic Chains

We show that the peak of an initially localized wave packet in one-dimensional nonlinear disordered chains decays more slowly than any power law of time. The systems under investigation are Klein-Gordon and nonlinear disordered Schrödinger-type chains, characterized by a harmonic onsite disordered potential and quartic nearest-neighbor coupling. Our results apply in the long-time limit, hold almost surely, and are valid for arbitrary finite energy values.

math-ph↗
arXiv2020

Subdiffusion in one-dimensional Hamiltonian chains with sparse interactions

We establish rigorously that transport is slower than diffusive for a class of disordered one-dimensional Hamiltonian chains. This is done by deriving quantitative bounds on the variance in equilibrium of the energy or particle current, as a function of time. The slow transport stems from the presence of rare insulating regions (Griffiths regions). In many-body disordered quantum chains, they correspond to regions of anomalously high disorder, where the system is in a localized phase. In contrast, we deal with quantum and classical disordered chains where the interactions, usually referred to as anharmonic couplings in classical systems, are sparse. The system hosts thus rare regions with no interactions and, since the chain is Anderson localized in the absence of interactions, the non-interacting rare regions are insulating. Part of the mathematical interest of our model is that it is one of the few non-integrable models where the diffusion constant can be rigorously proven not to be infinite.

math-ph↗
arXiv2017

A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems

Prethermalization refers to the transient phenomenon where a system thermalizes according to a Hamiltonian that is not the generator of its evolution. We provide here a rigorous framework for quantum spin systems where prethermalization is exhibited for very long times. First, we consider quantum spin systems under periodic driving at high frequency $ν$. We prove that up to a quasi-exponential time $τ_* \sim e^{c \fracν{\log^3 ν}}$, the system barely absorbs energy. Instead, there is an effective local Hamiltonian $\hat D$ that governs the time evolution up to $τ_*$, and hence this effective Hamiltonian is a conserved quantity up to $τ_*$. Next, we consider systems without driving, but with a separation of energy scales in the Hamiltonian. A prime example is the Fermi-Hubbard model where the interaction $U$ is much larger than the hopping $J$. Also here we prove the emergence of an effective conserved quantity, different from the Hamiltonian, up to a time $τ_*$ that is (almost) exponential in $U/J$.

math-ph↗
arXiv2016

Step Heat Profile in Localized Chains

We consider two types of strongly disordered one-dimensional Hamiltonian systems coupled to baths (energy or particle reservoirs) at the boundaries: strongly disordered quantum spin chains and disordered classical harmonic oscillators. These systems are believed to exhibit localization, implying in particular that the conductivity decays exponentially in the chain length $L$. We ask however for the profile of the (very slowly) transported quantity in the steady state. We find that this profile is a step-function, jumping in the middle of the chain from the value set by the left bath to the value set by the right bath. The width of the step grows not faster than $\sqrt{L}$. This is confirmed by numerics on a disordered quantum spin chain of 9 spins and on much longer chains of harmonic oscillators. In the case of harmonic oscillators, we also observe a drastic breakdown of local equilibrium at the step, resulting in a chaotic temperature profile.

cond-mat.stat-mech↗
arXiv2016

Absence of many-body mobility edges

Localization transitions as a function of temperature require a many-body mobility edge in energy, separating localized from ergodic states. We argue that this scenario is inconsistent because local fluctuations into the ergodic phase within the supposedly localized phase can serve as mobile bubbles that induce global delocalization. Such fluctuations inevitably appear with a low but finite density anywhere in any typical state. We conclude that the only possibility for many-body localization to occur are lattice models that are localized at all energies. Building on a close analogy with a model of assisted two-particle hopping, where interactions induce delocalization, we argue why hot bubbles are mobile and do not localize upon diluting their energy. Numerical tests of our scenario show that previously reported mobility edges cannot be distinguished from finite-size effects.

cond-mat.dis-nn↗
arXiv2014

Scenario for delocalization in translation invariant systems

We investigate the possibility of Many-Body Localization in translation invariant Hamiltonian systems, which was recently brought up by several authors. A key feature of Many-Body Localized disordered systems is recovered, namely the fact that resonant spots are rare and far-between. However, we point out that resonant spots are mobile, unlike in models with strong quenched disorder, and that these mobile spots constitute a possible mechanism for delocalization, albeit possibly only on very long timescales. In some models, this argument for delocalization can be made very explicit in first order of perturbation theory in the hopping. For models where this does not work, we present instead a non-perturbative argument that relies solely on ergodicity inside the resonant spots.

cond-mat.stat-mech↗
arXiv2014

Green-Kubo formula for weakly coupled system with dynamical noise

We study the Green-Kubo (GK) formula $κ(\varepsilon, ξ)$ for the heat conductivity of an infinite chain of $d$-dimensional finite systems (cells) coupled by a smooth nearest neighbour potential $\varepsilon V$. The uncoupled systems evolve according to Hamiltonian dynamics perturbed stochastically by an energy conserving noise of strength $ξ$. Noting that $κ(\varepsilon, ξ)$ exists and is finite whenever $ξ> 0$, we are interested in what happens when the strength of the noise $ξ\to 0$. For this, we start in this work by formally expanding $κ(\varepsilon, ξ)$ in a power series in $\varepsilon$, $κ(\varepsilon, ξ) = \varepsilon^2 \sum_{n\ge 2} \varepsilon^{n-2} κ_n (ξ)$ and investigating the (formal) equations satisfied by $κ_n (ξ$. We show in particular that $κ_2 (ξ)$ is well defined when no pinning potential is present, and coincides formally with the heat conductivity obtained in the weak coupling (van Hove) limit, where time is rescaled as $\varepsilon^{-2}t$, for the cases where the latter has been established \cite{LO, DL}. For one-dimensional systems, we investigate $κ_2 (ξ)$ as $ξ\to 0$ in three cases: the disordered harmonic chain, the rotor chain and a chain of strongly anharmonic oscillators. Moreover, we formally identify $κ_2 (ξ)$ with the conductivity obtained by having the chain between two reservoirs at temperature $T$ and $T+δT$, in the limit $δT\to 0$, $N \to \infty$, $\varepsilon \to 0$.

cond-mat.stat-mech↗