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Detailed view Article in peer-reviewed journal
Journal of the American Mathematical Society 25 (2012) (2011) 555-583
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Toward the Fourier law for a weakly interacting anharmonic crystal
Carlangelo Liverani1, Stefano Olla2, 3

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.
1:  DIPMAT - Dipartimento di Matematica [Roma II]
2:  CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3:  INRIA Paris - Rocquencourt - MICMAC
Weak coupling – scaling limits – hypoellipticity – hypocoercivity – Ginzburg-Landau dynamics – heat equation