Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noise

Marielle Simon
INRIA Lille
http://chercheurs.lille.inria.fr/masimon/index.html

Date(s) : 10/05/2019   iCal
11 h 00 min - 12 h 00 min

We investigate the macroscopic behavior of the disordered harmonic chain of oscillators, through energy diffusion. The Hamiltonian dynamics of the system is perturbed by a degenerate conservative noise. After rescaling space and time diffusively, we prove that energy fluctuations in equilibrium evolve according to a linear heat equation. The diffusion coefficient is obtained from the non-gradient Varadhan’s approach, and is equivalently defined through the Green-Kubo formula. Since the perturbation is very degenerate and the symmetric part of the generator does not have a spectral gap, the standard non-gradient method is reviewed under new perspectives.

https://hal.inria.fr/hal-01065976v3

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