Thermal conductivity in harmonic lattices with random collisions
Abstract
We review recent rigorous mathematical results about the macroscopic behaviour of harmonic chains with the dynamics perturbed by a random exchange of velocities between nearest neighbor particles. The random exchange models the effects of nonlinearities of anharmonic chains and the resulting dynamics have similar macroscopic behaviour. In particular there is a superdiffusion of energy for unpinned acoustic chains. The corresponding evolution of the temperature profile is governed by a fractional heat equation. In non-acoustic chains we have normal diffusivity, even if momentum is conserved.
Cite
@article{arxiv.1509.02474,
title = {Thermal conductivity in harmonic lattices with random collisions},
author = {Giada Basile and Cédric Bernardin and Milton Jara and Tomasz Komorowski and Stefano Olla},
journal= {arXiv preprint arXiv:1509.02474},
year = {2015}
}
Comments
Review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.)