Wigner functions and stochastically perturbed lattice dynamics

Giada Basile (1) , Stefano Olla (2) , Herbert Spohn (3)

1 WIAS - Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin]
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 D-MUTU-ZM - Centre fo Mathematical Sciences

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 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.

Mots clés: Wigner functions; Lattice dynamics; conservative stochastic dynamics

Domaines: Probabilités [math.PR]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]

Giada Basile, Stefano Olla, Herbert Spohn. Wigner functions and stochastically perturbed lattice dynamics. 2008. ⟨hal-00280839v1⟩