English

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

Probability 2020-10-23 v7

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.

Keywords

Cite

@article{arxiv.1402.3617,
  title  = {Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noise},
  author = {Clément Erignoux and Marielle Simon},
  journal= {arXiv preprint arXiv:1402.3617},
  year   = {2020}
}