Toward the Fourier law for a weakly interacting anharmonic crystal

Liverani, Carlangelo; Olla, Stefano

doi:10.1090/S0894-0347-2011-00724-8

Toward the Fourier law for a weakly interacting anharmonic crystal
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by Carlangelo Liverani and Stefano Olla

J. Amer. Math. Soc. 25 (2012), 555-583

DOI: https://doi.org/10.1090/S0894-0347-2011-00724-8

Published electronically: December 1, 2011

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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 turns out that this macroscopic evolution is given by the so-called conservative (nongradient) Ginzburg-Landau system of stochastic differential equations. The proof exploits hypocoercivity and hypoellipticity properties of the uncoupled dynamics.

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