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Green-Kubo formula for weakly coupled systems with noise

hal.structure.identifierLaboratoire Jean Alexandre Dieudonné [JAD]
dc.contributor.authorBernardin, Cédric
HAL ID: 7637		*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorHuveneers, François*
hal.structure.identifierCenter for Mathematical Sciences Research
dc.contributor.authorLebowitz, Joel L.*
hal.structure.identifierDipartimento di Matematica [Roma II] [DIPMAT]
dc.contributor.authorLiverani, Carlangelo*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorOlla, Stefano
HAL ID: 18345
ORCID: 0000-0003-0845-1861		*
dc.date.accessioned2014-01-15T13:31:21Z
dc.date.available2014-01-15T13:31:21Z
dc.date.issued2015
dc.identifier.issn0010-3616
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12443
dc.language.isoenen
dc.subjectthermal conductivity
dc.subjectsmall noise
dc.subjectcoupling expansion
dc.subjectGreen-Kubo formula
dc.subject.ddc520en
dc.titleGreen-Kubo formula for weakly coupled systems with noise
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDipartimento di Matematica [Roma II] (DIPMAT) http://www.mat.uniroma2.it/ Universita degli studi di Roma Tor Vergata;Italie
dc.contributor.editoruniversityotherLaboratoire Jean Alexandre Dieudonné (JAD) http://math.unice.fr/ CNRS : UMR7351 – Université Nice Sophia Antipolis [UNS];France
dc.description.abstractenWe 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.isversionofjnlnameCommunications in Mathematical Physics
dc.relation.isversionofjnlvol334
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages1377-1412
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00220-014-2206-7
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-09-11T15:08:04Z
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