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Article Dans Une Revue Communications in Mathematical Physics Année : 2009

Thermal Conductivity for a Momentum Conserving Model

Résumé

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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Dates et versions

hal-00017718 , version 1 (24-01-2006)
hal-00017718 , version 2 (05-04-2006)
hal-00017718 , version 3 (29-01-2008)
hal-00017718 , version 4 (02-07-2008)
hal-00017718 , version 5 (02-08-2008)

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Citer

Giada Basile, Cedric Bernardin, Stefano Olla. Thermal Conductivity for a Momentum Conserving Model. Communications in Mathematical Physics, 2009, 287 (1), pp.67-98. ⟨10.1007/s00220-008-0662-7⟩. ⟨hal-00017718v5⟩
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