Abstract
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 an on-site harmonic potential is present. This implies a finite conductivity in d ≥ 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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Communicated by A. Kupiainen
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Basile, G., Bernardin, C. & Olla, S. Thermal Conductivity for a Momentum Conservative Model. Commun. Math. Phys. 287, 67–98 (2009). https://doi.org/10.1007/s00220-008-0662-7
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DOI: https://doi.org/10.1007/s00220-008-0662-7