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arXiv · 1402.3617

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

Clément Erignoux·Marielle Simon
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Abstract

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.

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Clément Erignoux, Marielle Simon. 2014-02-14. Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noise. https://doi.org/10.1214/19-ejp399

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