title: Momentum conserving model with anomalous thermal conductivity in low dimensional systems.
abstract: 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 > or = 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.
authors.affiliation: Dipartimento di Matematica, Università di Firenze, Viale Morgagni 67a, 50134 Firenze, Italy.
authors.forename: Giada
authors.initials: G
authors.lastname: Basile
authors.forename: Cédric
authors.initials: C
authors.lastname: Bernardin
authors.forename: Stefano
authors.initials: S
authors.lastname: Olla