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Equilibrium fluctuation for an anharmonic chain with boundary conditions in the Euler scaling limit

Olla, Stefano; Xu, Lu (2019), Equilibrium fluctuation for an anharmonic chain with boundary conditions in the Euler scaling limit. https://basepub.dauphine.fr/handle/123456789/18573

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-01971506
Date
2019
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
27
Metadata
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Author(s)
Olla, Stefano cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Xu, Lu
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We study the evolution in equilibrium of the fluctuations for the conserved quantities of a chain of anharmonic oscillators in the hyperbolic space-time scaling. Boundary conditions are determined by applying a constant tension at one side, while the position of the other side is kept fixed. The Hamiltonian dynamics is perturbed by random terms conservative of such quantities. We prove that these fluctuations evolve macroscopically following the linearized Euler equations with the corresponding boundary conditions, even in some time scales larger than the hyperbolic one.
Subjects / Keywords
Hydrodynamic Fluctuations; Compressible Euler equation