Anomalous large thermal conductivity has been observed numerically and experimentally in one- and two-dimensional systems. There is an open debate about the role of conservation of momentum. We introduce a model whose thermal conductivity diverges in dimensions 1 and 2 if momentum is conserved, while it remains finite in dimension d >= 3. We consider a system of harmonic oscillators perturbed by a nonlinear stochastic dynamics conserving momentum and energy. We compute explicitly the time correlation function of the energy current C-J(t), and we find that it behaves, for large time, like t(-d/2) in the unpinned cases, and like t(-d/2-1) when an on-site harmonic potential is present. This result clarifies the role of conservation of momentum in the anomalous thermal conductivity in low dimensions.
Momentum conserving model with anomalous thermal conductivity in low dimensional systems / Basile, Giada; Cedric, Bernardin; Stefano, Olla. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - STAMPA. - 96:20(2006), pp. 204303-1-204303-4. [10.1103/physrevlett.96.204303]