| dc.contributor.author | Bernardin, Cédric | * |
| dc.contributor.author | Huveneers, François | * |
| dc.contributor.author | Lebowitz, Joel L. | * |
| dc.contributor.author | Liverani, Carlangelo | * |
| dc.contributor.author | Olla, Stefano | * |
| 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.person.labIds | 199970 | * |
| hal.person.labIds | 60 | * |
| hal.person.labIds | 73173 | * |
| hal.person.labIds | 15788 | * |
| hal.person.labIds | 60 | * |
