Thermal Conductivity for a Momentum Conserving Model

Details Thermal Conductivity for a Momentum Conserving Model Thermal Conductivity for a Momentum Conserving Model

2006-01-24

arxiv.org/abs/cond-mat/0601544v5

Communications in Mathematical Physics 287, 1 (2009) 67-98

Physics

Condensed Matter

Statistical Mechanics

Accepted for the publication in Communications in Mathematical Physics

Scientific paper

10.1007/s00220-008-0662-7

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 oscillators perturbed by a stochastic dynamics conserving momentum and energy. We compute thermal conductivity via Green-Kubo formula. In the harmonic case we compute the current-current time correlation function, that decay like $t^{-d/2}$ in the unpinned case and like $t^{-d/2-1}$ if a on-site harmonic potential is present. This implies a finite conductivity in $d\ge 3$ or in pinned cases, and we compute it explicitly. For general anharmonic strictly convex interactions we prove some upper bounds for the conductivity that behave qualitatively as in the harmonic cases.

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