Thermal Conductivity for a Momentum Conserving Model
Résumé
We present here complete mathematical proofs of the results annouced in cond-mat/0509688. 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 harmonic oscillators perturbed by a stochastic dynamics conserving momentum and energy. We compute the current-current time correlation function and the thermal conductivity via Green-Kubo formula. We prove that the current-current time correlation function decay like $t^{-d/2}$ in the unpinned case and like $t^{-d/2-1}$ if a on-site harmonic potential is present.