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2019 Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noise
Clément Erignoux, Marielle Simon
Electron. J. Probab. 24: 1-52 (2019). DOI: 10.1214/19-EJP399

Abstract

We investigate the macroscopic energy diffusion of a disordered harmonic chain of oscillators, whose hamiltonian dynamics is perturbed by a degenerate conservative noise. After rescaling space and time diffusively, we prove that the equilibrium energy fluctuations evolve according to a linear heat equation. The diffusion coefficient is obtained from Varadhan’s non-gradient 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. "Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noise." Electron. J. Probab. 24 1 - 52, 2019. https://doi.org/10.1214/19-EJP399

Information

Received: 7 December 2018; Accepted: 27 November 2019; Published: 2019
First available in Project Euclid: 20 December 2019

zbMATH: 07149383
MathSciNet: MR4049079
Digital Object Identifier: 10.1214/19-EJP399

Subjects:
Primary: 60K35
Secondary: 82C22

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