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Kinetic limit for a chain of harmonic oscillators with a point Langevin thermostat

hal.structure.identifierInstitut of Mathematics - Polish Academy of Sciences [PAN]
dc.contributor.authorKomorowski, Tomasz
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.accessioned2021-11-03T10:54:51Z
dc.date.available2021-11-03T10:54:51Z
dc.date.issued2020
dc.identifier.issn0022-1236
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22160
dc.language.isoenen
dc.subjectHarmonic chains with stochastic noiseen
dc.subjectWigner functionsen
dc.subjectLinear kinetic equation with interfaceen
dc.subjectDuhamel formulaen
dc.subject.ddc520en
dc.titleKinetic limit for a chain of harmonic oscillators with a point Langevin thermostaten
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe consider an infinite chain of coupled harmonic oscillators with a Langevin thermostat attached at the origin and energy, momentum and volume conserving noise that models the collisions between atoms. The noise is rarefied in the limit, that corresponds to the hypothesis that in the macroscopic unit time only a finite number of collisions takes place (Boltzmann-Grad limit). We prove that, after the hyperbolic space-time rescaling, the Wigner distribution, describing the energy density of phonons in space-frequency domain, converges to a positive energy density function W (t, y, k) that evolves according to a linear kinetic equation, with the interface condition at y = 0 that corresponds to reflection, transmission and absorption of phonons. The paper extends the results of [3], where a thermostatted harmonic chain (with no inter-particle scattering) has been considered.en
dc.relation.isversionofjnlnameJournal of Functional Analysis
dc.relation.isversionofjnlvol279en
dc.relation.isversionofjnlissue12en
dc.relation.isversionofjnldate2020-12
dc.relation.isversionofdoi10.1016/j.jfa.2020.108764en
dc.relation.isversionofjnlpublisherElsevieren
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2021-11-03T10:52:34Z
hal.author.functionaut
hal.author.functionaut


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