hal.structure.identifier Laboratoire Jean Alexandre Dieudonné [JAD] dc.contributor.author Bernardin, Cédric HAL ID: 7637 * hal.structure.identifier CEntre de REcherches en MAthématiques de la DEcision [CEREMADE] dc.contributor.author Huveneers, François * hal.structure.identifier Center for Mathematical Sciences Research dc.contributor.author Lebowitz, Joel L. * hal.structure.identifier Dipartimento di Matematica [Roma II] [DIPMAT] dc.contributor.author Liverani, Carlangelo * hal.structure.identifier CEntre de REcherches en MAthématiques de la DEcision [CEREMADE] dc.contributor.author Olla, Stefano HAL ID: 18345 ORCID: 0000-0003-0845-1861 * dc.date.accessioned 2014-01-15T13:31:21Z dc.date.available 2014-01-15T13:31:21Z dc.date.issued 2015 dc.identifier.issn 0010-3616 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/12443 dc.language.iso en en dc.subject thermal conductivity dc.subject small noise dc.subject coupling expansion dc.subject Green-Kubo formula dc.subject.ddc 520 en dc.title Green-Kubo formula for weakly coupled systems with noise dc.type Article accepté pour publication ou publié dc.contributor.editoruniversityother Dipartimento di Matematica [Roma II] (DIPMAT) http://www.mat.uniroma2.it/ Universita degli studi di Roma Tor Vergata;Italie dc.contributor.editoruniversityother Laboratoire Jean Alexandre Dieudonné (JAD) http://math.unice.fr/ CNRS : UMR7351 – Université Nice Sophia Antipolis [UNS];France dc.description.abstracten We consider an infinite system of cells coupled into a chain by a smooth nearest neighbour potential $\varepsilon V$. The uncoupled system (cells) evolve according to Hamiltonian dynamics perturbed stochastically with an energy conserving noise of strength $\zeta$. We study the Green-Kubo (GK) formula $\kappa(\varepsilon,\zeta)$ for the heat conductivity of this system which exists and is finite for $\zeta >0$, by formally expanding $\kappa(\varepsilon,\zeta)$ in a power series in $\varepsilon$, $\kappa(\varepsilon,\zeta) = \sum_{n\ge 2} \varepsilon^n \kappa_n(\zeta)$. We show that $\kappa_2(\zeta)$ is the same as the conductivity obtained in the weak coupling (van Hove) limit where time is rescaled as $\varepsilon^{-2}t$. $\kappa_2(\zeta)$ is conjectured to approach as $\zeta \to 0$ a value proportional to that obtained for the weak coupling limit of the purely Hamiltonian chain. We also show that the $\kappa_2(\zeta)$ from the GK formula, is the same as the one obtained from the flux of an open system in contact with Langevin reservoirs. Finally we show that the limit $\zeta\to 0$ of $\kappa_2(\zeta)$ is finite for the pinned anharmonic oscillators due to phase mixing caused by the non-resonating frequencies of the neighbouring cells. This limit is bounded for coupled rotors and vanishes for harmonic chain with random pinning. dc.relation.isversionofjnlname Communications in Mathematical Physics dc.relation.isversionofjnlvol 334 dc.relation.isversionofjnlissue 3 dc.relation.isversionofjnldate 2015 dc.relation.isversionofjnlpages 1377-1412 dc.relation.isversionofdoi http://dx.doi.org/10.1007/s00220-014-2206-7 dc.relation.isversionofjnlpublisher Springer dc.subject.ddclabel Sciences connexes (physique, astrophysique) en dc.description.submitted non en dc.description.ssrncandidate non dc.description.halcandidate oui dc.description.readership recherche dc.description.audience International dc.relation.Isversionofjnlpeerreviewed oui dc.date.updated 2017-09-11T15:08:04Z hal.author.function aut hal.author.function aut hal.author.function aut hal.author.function aut hal.author.function aut
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