Geodesic
Toward the Fourier law for a weakly interacting anharmonic crystal
Liverani, Carlangelo1 ; Olla, Stefano2
1 Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma, Italy
2 CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, 75775 Paris-Cedex 16, France and INRIA - Université Paris Est, CERMICS, Projet MICMAC, Ecole des Ponts ParisTech, 6 & 8 Av. Pascal, 77455 Marne-la-Vallée Cedex 2, France
Journal of the American Mathematical Society, Tome 25 (2012) no. 2, pp. 555-583

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-2011-00724-8

Liverani, Carlangelo 1 ; Olla, Stefano 2

1 Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma, Italy
2 CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, 75775 Paris-Cedex 16, France and INRIA - Université Paris Est, CERMICS, Projet MICMAC, Ecole des Ponts ParisTech, 6 & 8 Av. Pascal, 77455 Marne-la-Vallée Cedex 2, France 
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Liverani, Carlangelo; Olla, Stefano. Toward the Fourier law for a weakly interacting anharmonic crystal. Journal of the American Mathematical Society, Tome 25 (2012) no. 2, pp. 555-583. doi: 10.1090/S0894-0347-2011-00724-8

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