Toward the Fourier law for a weakly interacting anharmonic crystal

Details Toward the Fourier law for a weakly interacting anharmonic crystal Toward the Fourier law for a weakly interacting anharmonic crystal

2010-06-15

arxiv.org/abs/1006.2900v1

Mathematics

Probability

Scientific paper

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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