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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

Keyword(s) : Weak coupling – scaling limits – hypoellipticity – hypocoercivity – Ginzburg-Landau dynamics – heat equation

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From: Stefano Olla <>

Submitted on: Monday, 14 June 2010 19:04:41

Updated on: Tuesday, 10 January 2012 18:24:02