Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-09-27
Physical Review Letters 96 (2006) 204303
Physics
Condensed Matter
Statistical Mechanics
Scientific paper
10.1103/PhysRevLett.96.204303
Anomalous large thermal conductivity has been observed numerically and experimentally in one and two dimensional systems. All explicitly solvable microscopic models proposed to date 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 if momentum is conserved, while it remains finite in dimension $d\ge 3$. We consider a system of harmonic oscillators perturbed by a non-linear 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. Consequently thermal conductivity is finite if $d\ge 3$ or if an on-site potential is present, while it is infinite in the other cases. This result clarifies the role of conservation of momentum in the anomalous thermal conductivity in low dimensions.
Basile Giada
Bernardin Cédric
Olla Stefano
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