A momentum conserving model with anomalous thermal conductivity in low dimension
Résumé
Anomalous large thermal conductivity has been observed numerically and experimentally in one and two dimensional systems. All explicitly solvable microscopic models proposed until now did not explain this phenomenon and there is an open debate about the role of conservation of momentum. We introduce a model whose thermal conductivity diverges in dimension 1 and 2, while it remains finite in dimension 3. We compute the finite-size thermal conductivity of a system of harmonic oscillators perturbed by a non-linear stochastic dynamics conserving momentum and energy. In the limit as the size N of the system goes to infinity, conductivity diverges like N in dimension 1 and like ln N in dimension 2. Conductivity remains finite if d=3 or if a pinning (on site potential) is present. This result clarifies the role of conservation of momentum in the anomalous thermal conductivity.