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.
Liverani, C., Olla, S. (2012). Toward the Fourier law for a weakly interacting anharmonic crystal. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 25(2), 555-583 [10.1090/S0894-0347-2011-00724-8].
Toward the Fourier law for a weakly interacting anharmonic crystal
LIVERANI, CARLANGELO;
2012-01-01
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.File | Dimensione | Formato | |
---|---|---|---|
jams-2011.pdf
solo utenti autorizzati
Licenza:
Copyright dell'editore
Dimensione
383.75 kB
Formato
Adobe PDF
|
383.75 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.