Thermal Conductivity for a Momentum Conserving Model

Giada Basile (1) , Cedric Bernardin (2) , Stefano Olla (3)

1 WIAS - Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin]
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We introduce a model whose thermal conductivity diverges in dimension 1 and 2, while it remains finite in dimension 3. We consider a system of oscillators perturbed by a stochastic dynamics conserving momentum and energy. We compute thermal conductivity via Green-Kubo formula. In the harmonic case we compute the current-current time correlation function, that decay like $t^{-d/2}$ in the unpinned case and like $t^{-d/2-1}$ if a on-site harmonic potential is present. This implies a finite conductivity in $d\ge 3$ or in pinned cases, and we compute it explicitly. For general anharmonic strictly convex interactions we prove some upper bounds for the conductivity that behave qualitatively as in the harmonic cases.

Mots clés: Thermal conductivity; Green-Kubo formula; anomalous heat transport; Fourier's law; non-equilibrium systems.; non-equilibrium systems

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

Giada Basile, Cedric Bernardin, Stefano Olla. Thermal Conductivity for a Momentum Conserving Model. 2008. ⟨hal-00017718v4⟩