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

TL;DR

This paper studies how a chain of anharmonic oscillators with random velocity flips reaches stationary states and explores how tension gradients influence thermal conductivity, providing bounds and linear response properties.

Contribution

It introduces a model with energy-conserving random velocity flips and analyzes the resulting stationary states, entropy production, and thermal conductivity bounds.

Findings

Existence of the Onsager matrix via Green-Kubo formulas

Explicit bounds on thermal conductivity depending on temperature

Analysis of entropy production in stationary states

Abstract

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 $\tau_\ell$ and $\tau_r$. If the forces differ $\tau_\ell \neq \tau_r$ 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.