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dc.contributor.authorGualdani, Maria Pia
dc.contributor.authorGamba, Irene M.
dc.contributor.authorMischler, Stéphane
dc.contributor.authorSparber, Christof
dc.contributor.authorArnold, Anton
dc.contributor.authorMouhot, Clément
HAL ID: 1892
dc.date.accessioned2010-11-02T14:20:27Z
dc.date.available2010-11-02T14:20:27Z
dc.date.issued2012
dc.identifier.issn0218-2025
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/4980
dc.language.isoenen
dc.subjectWigner transform
dc.subjectStationary solution
dc.subjectLarge time behavior
dc.subjectFokker Planck operator
dc.subjectSpectral gap
dc.subject.ddc515en
dc.titleThe Wigner-Fokker-Planck equation: Stationary states and large time behavior
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherDepartment of Mathematics, Statistics, and Computer Science University of Illinois at Chicago;États-Unis
dc.contributor.editoruniversityotherDepartement of Mathematics (UT, USA);États-Unis
dc.contributor.editoruniversityotherInstitut für Analysis und Scientific Computing, Wien;Autriche
dc.description.abstractenWe consider the linear Wigner-Fokker-Planck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential. For a certain class of perturbations we prove that the equation admits a unique stationary solution in a weighted Sobolev space. A key ingredient of the proof is a new result on the existence of spectral gaps for Fokker-Planck type operators in certain weighted $L^2$--spaces. In addition we show that the steady state corresponds to a positive density matrix operator with unit trace and that the solutions of the time-dependent problem converge towards the steady state with an exponential rate.
dc.relation.isversionofjnlnameMathematical Models and Methods in Applied Sciences
dc.relation.isversionofjnlvol22
dc.relation.isversionofjnlissue11
dc.relation.isversionofjnldate2012
dc.relation.isversionofjnlpagesn°1250034
dc.relation.isversionofdoihttp://dx.doi.org/10.1142/S0218202512500340
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherWorld Scientific
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-09-21T12:56:37Z


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