Hyperbolic scaling limit of non-equilibrium fluctuations for a weakly anharmonic chain
Xu, Lu (2019), Hyperbolic scaling limit of non-equilibrium fluctuations for a weakly anharmonic chain. https://basepub.dauphine.fr/handle/123456789/20487
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-02384423
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We consider a chain of n coupled oscillators placed on a one-dimensional lattice with periodic boundary conditions. The interaction between particles is determined by a weakly anharmonic potential Vn = r 2 /2 + σnU (r), where U has bounded second derivative and σn vanishes as n → ∞. The dynamics is perturbed by noises acting only on the positions, such that the total momentum and length are the only conserved quantities. With relative entropy technique, we prove for dynamics out of equilibrium that, if σn decays sufficiently fast, the fluctuation field of the conserved quantities converges in law to a linear p-system in the hyperbolic space-time scaling limit. The transition speed is spatially homogeneous due to the vanishing anharmonicity. We also present a quantitative bound for the speed of convergence to the corresponding hydrodynamic limit.
Subjects / KeywordsHyperbolic scaling limit
Showing items related by title and author.