Energy transport in stochastically perturbed lattice dynamics

Basile, Giada; Olla, Stefano; Spohn, Herbert

Basile, Giada; Olla, Stefano; Spohn, Herbert (2010), Energy transport in stochastically perturbed lattice dynamics, Archive for Rational Mechanics and Analysis, 195, 1, p. 171-203. http://dx.doi.org/10.1007/s00205-008-0205-6

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00280839/en/

Date

2010

Journal name

Archive for Rational Mechanics and Analysis

Volume

195

Number

Publisher

Springer

Pages

171-203

Abstract (EN)

We consider lattice dynamics with a small stochastic perturbation of order ε and prove that for a space-time scale of order ε−1 the local spectral density (Wigner function) evolves according to a linear transport equation describing inelastic collisions. For an energy and momentum conserving chain the transport equation predicts a slow decay, as 1/√t, for the energy current correlation in equilibrium. This is in agreement with previous studies using a different method.

Subjects / Keywords

Wigner functions; semiclassical limits; lattice dynamics; conservative stochastic dynamics; phonon Boltzmann equation; energy transport