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Toward the Fourier law for a weakly interacting anharmonic crystal

Abstract : For a system of weakly interacting anharmonic oscillators, perturbed by an energy preserving stochastic dynamics, we prove an autonomous (stochastic) evolution for the energies at large time scale (with respect to the coupling parameter). It turn out that this macroscopic evolution is given by the so called conservative (non-gradient) Ginzburg-Landau system of stochastic differential equations. The proof exploits hypocoercivity and hypoellipticity properties of the uncoupled dynamics.
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https://hal.archives-ouvertes.fr/hal-00492016
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Submitted on : Monday, June 14, 2010 - 7:04:41 PM
Last modification on : Friday, February 4, 2022 - 3:09:42 AM
Long-term archiving on: : Tuesday, September 14, 2010 - 8:16:13 PM

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Carlangelo Liverani, Stefano Olla. Toward the Fourier law for a weakly interacting anharmonic crystal. Journal of the American Mathematical Society, 2011, 25 (2012), pp.555-583. ⟨10.1090/S0894-0347-2011-00724-8⟩. ⟨hal-00492016⟩

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