Thermal Conductivity for a Momentum Conserving Model
Résumé
We present here complete mathematical proofs of the results announced 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 nite-size thermal conductivity via Green-Kubo formula. In the limit as the size N of the system goes to in nity, conductivity diverges like N in dimension 1 and like lnN in dimension 2. Conductivity remains finite if dimesion is 3 or higher or if a pinning (on site potential) is present.