Title :

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

Author(s) :

Erignoux, Clement [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Simon, Marielle [Auteur correspondant]
Systèmes de particules et systèmes dynamiques [Paradyse]

Journal title :

Electronic Journal of Probability

Publisher :

Institute of Mathematical Statistics (IMS)

Publication date :

2019

ISSN :

1083-6489

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Physique mathématique [math-ph]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Diffusion de l'énergie dans des systèmes hamiltoniens bruitésés

Comment :

One major correction has been done. An author has been added

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL