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Cedric Bernardin

Publications and source records attributed to Cedric Bernardin.

28 records · Page 2Linked to original sources
arXiv2012

Transport Properties of a Chain of Anharmonic Oscillators with random flip of velocities

We consider the stationary states of a chain of $n$ anharmonic coupled oscillators, whose deterministic hamiltonian dynamics is perturbed by random independent sign change of the velocities (a random mechanism that conserve energy). The extremities are coupled to thermostats at different temperature $T_\ell$ and $T_r$ and subject to constant forces $τ_\ell$ and $τ_r$. If the forces differ $τ_\ell \neq τ_r$ the center of mass of the system will move of a speed $V_s$ inducing a tension gradient inside the system. Our aim is to see the influence of the tension gradient on the thermal conductivity. We investigate the entropy production properties of the stationary states, and we prove the existence of the Onsager matrix defined by Green-kubo formulas (linear response). We also prove some explicit bounds on the thermal conductivity, depending on the temperature.

cond-mat.stat-mech↗
arXiv2011

Nonequilibrium Stationary States of Harmonic Chains with Bulk Noises

We consider a chain composed of $N$ coupled harmonic oscillators in contact with heat baths at temperature $T_\ell$ and $T_r$ at sites 1 and $N$ respectively. The oscillators are also subjected to non-momentum conserving bulk stochastic noises. These make the heat conductivity satisfy Fourier's law. Here we describe some new results about the hydrodynamical equations for typical macroscopic energy and displacement profiles, as well as their fluctuations and large deviations, in two simple models of this type.

cond-mat.stat-mech↗
arXiv2011

A simple particle model for a system of coupled equations with absorbing collision term

We study a particle model for a simple system of partial differential equations describing, in dimension $d\geq 2$, a two component mixture where light particles move in a medium of absorbing, fixed obstacles; the system consists in a transport and a reaction equation coupled through pure absorption collision terms. We consider a particle system where the obstacles, of radius $\var$, become inactive at a rate related to the number of light particles travelling in their range of influence at a given time and the light particles are instantaneously absorbed at the first time they meet the physical boundary of an obstacle; elements belonging to the same species do not interact among themselves. We prove the convergence (a.s. w.r.t. the product measure associated to the initial datum for the light particle component) of the densities describing the particle system to the solution of the system of partial differential equations in the asymptotics $ a_n^d n^{-κ}\to 0$ and $a_n^d \var^ζ\to 0$, for $κ\in(0,\frac 12)$ and $ζ\in (0,\frac12 - \frac 1{2d})$, where $a_n^{-1}$ is the effective range of the obstacles and $n$ is the total number of light particles.

cond-mat.stat-mech↗
arXiv2008

Thermal Conductivity for a Noisy Disordered Harmonic Chain

We consider a $d$-dimensional disordered harmonic chain (DHC) perturbed by an energy conservative noise. We obtain uniform in the volume upper and lower bounds for the thermal conductivity defined through the Green-Kubo formula. These bounds indicate a positive finite conductivity. We prove also that the infinite volume homogenized Green-Kubo formula converges.

cond-mat.stat-mech↗
arXiv2008

Superdiffusivity of Asymmetric Energy Model in Dimension One and Two

We discuss an asymmetric energy model (AEM) introduced by Giardina et al. in \cite{7}. This model is expected to belong to the KPZ class. We obtain lower bounds for the diffusion coefficient. In particular, the diffusion coefficient is diverging in dimension one and two as it is expected in the KPZ picture.

cond-mat.stat-mech↗
arXiv2008

Stationary non-equilibrium properties for a heat conduction model

We consider a stochastic heat conduction model for solids composed by N interacting atoms. The system is in contact with two heat baths at different temperature $T_\ell$ and $T_r$. The bulk dynamics conserve two quantities: the energy and the deformation between atoms. If $T_\ell \neq T_r$, a heat flux takes place in the system. For large $N$, the system adopts a linear temperature profile between $T_\ell$ and $T_r$. We establish the hydrodynamic limit for the two conserved quantities. We introduce the fluctuations field of the energy and of the deformation in the non-equilibrium steady state. As $N$ goes to infinity, we show that this field converges to a Gaussian field and we compute the limiting covariance matrix. The main contribution of the paper is the study of large deviations for the temperature profile in the non-equilibrium stationary state. A variational formula for the rate function is derived following the recent macroscopic fluctuation theory of Bertini et al.

cond-mat.stat-mech↗
arXiv2008

Thermal Conductivity for a Momentum Conserving Model

We introduce a model whose thermal conductivity diverges in dimension 1 and 2, while it remains finite in dimension 3. We consider a system of oscillators perturbed by a stochastic dynamics conserving momentum and energy. We compute thermal conductivity via Green-Kubo formula. In the harmonic case we compute the current-current time correlation function, that decay like $t^{-d/2}$ in the unpinned case and like $t^{-d/2-1}$ if a on-site harmonic potential is present. This implies a finite conductivity in $d\ge 3$ or in pinned cases, and we compute it explicitly. For general anharmonic strictly convex interactions we prove some upper bounds for the conductivity that behave qualitatively as in the harmonic cases.

cond-mat.stat-mech↗
arXiv2006

A momentum conserving model with anomalous thermal conductivity in low dimension

Anomalous large thermal conductivity has been observed numerically and experimentally in one and two dimensional systems. All explicitly solvable microscopic models proposed to date did not explain this phenomenon and there is an open debate about the role of conservation of momentum. We introduce a model whose thermal conductivity diverges in dimension 1 and 2 if momentum is conserved, while it remains finite in dimension $d\ge 3$. We consider a system of harmonic oscillators perturbed by a non-linear stochastic dynamics conserving momentum and energy. We compute explicitly the time correlation function of the energy current $C\_J(t)$, and we find that it behaves, for large time, like $t^{-d/2}$ in the unpinned cases, and like $t^{-d/2-1}$ when an on site harmonic potential is present. Consequently thermal conductivity is finite if $d\ge 3$ or if an on-site potential is present, while it is infinite in the other cases. This result clarifies the role of conservation of momentum in the anomalous thermal conductivity in low dimensions.

cond-mat.stat-mech↗