arXiv subjects

Cédric Bernardin

Publications and source records attributed to Cédric Bernardin.

22 records · Page 2Linked to original sources

arXiv2013

Small perturbation of a disordered harmonic chain by a noise and an anharmonic potential

We study the thermal properties of a pinned disordered harmonic chain weakly perturbed by a noise and an anharmonic potential. The noise is controlled by a parameter $λ\rightarrow 0$, and the anharmonicity by a parameter $λ' \le λ$. Let $κ$ be the conductivity of the chain, defined through the Green-Kubo formula. Under suitable hypotheses, we show that $κ= \mathcal O (λ)$ and, in the absence of anharmonic potential, that $κ\sim λ$. This is in sharp contrast with the ordered chain for which $κ\sim 1/λ$, and so shows the persitence of localization effects for a non-integrable dynamics.

math-ph↗

arXiv2013

Superdiffusion of energy in Hamiltonian systems perturbed by a conservative noise

We review some recent results on the anomalous diffusion of energy in systems of 1D coupled oscillators and we revisit the role of momentum conservation.

cond-mat.stat-mech↗

arXiv2013

Entropy of non-equilibrium stationary measures of boundary driven TASEP

We examine the entropy of non-equilibrium stationary states of boundary driven totally asymmetric simple exclusion processes. As a consequence, we obtain that the Gibbs-Shannon entropy of the non equilibrium stationary state converges to the Gibbs-Shannon entropy of the local equilibrium state. Moreover, we prove that its fluctuations are Gaussian, except when the mean displacement of particles produced by the bulk dynamics agrees with the particle flux induced by the density reservoirs in the maximal phase regime.

math.PR↗

arXiv2011

Anomalous diffusion for a class of systems with two conserved quantities

We introduce a class of one dimensional deterministic models of energy-volume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative stochastic noise so that it becomes ergodic. System of conservation laws are derived as hydrodynamic limits of the modified dynamics. Numerical evidence shows these models are still super-diffusive. This is proven rigorously for harmonic potentials.

cond-mat.stat-mech↗