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

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01065976
Contributor : Marielle Simon <>
Submitted on : Wednesday, February 6, 2019 - 8:57:08 PM
Last modification on : Friday, March 29, 2019 - 2:26:13 AM
Long-term archiving on : Tuesday, May 7, 2019 - 3:49:18 PM

File

Corr_18_11_2018-MS-clean.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01065976, version 3
  • ARXIV : 1402.3617

Collections

Citation

Clément Erignoux, Marielle Simon. Equilibrium fluctuations for the disordered harmonic chain perturbed by an energy conserving noise. 2014. ⟨hal-01065976v3⟩

Share

Metrics

Record views

45

Files downloads

48