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dc.contributor.authorARNOLD, ANTON
dc.contributor.authorGAMBA, IRENE M.
dc.contributor.authorGUALDANI, MARIA PIA
dc.contributor.authorMISCHLER, STÉPHANE
dc.contributor.authorMOUHOT, CLEMENT
dc.contributor.authorSPARBER, CHRISTOF
dc.date.accessioned2016-02-28T06:33:40Z
dc.date.available2016-02-28T06:33:40Z
dc.date.issued2012-09-10
dc.identifier.citationARNOLD A, GAMBA IM, GUALDANI MP, MISCHLER S, MOUHOT C, et al. (2012) THE WIGNER–FOKKER–PLANCK EQUATION: STATIONARY STATES AND LARGE TIME BEHAVIOR. Mathematical Models and Methods in Applied Sciences 22: 1250034. Available: http://dx.doi.org/10.1142/S0218202512500340.
dc.identifier.issn0218-2025
dc.identifier.issn1793-6314
dc.identifier.doi10.1142/S0218202512500340
dc.identifier.urihttp://hdl.handle.net/10754/599977
dc.description.abstractWe consider the linear WignerFokkerPlanck 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 FokkerPlanck 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. © 2012 World Scientific Publishing Company.
dc.description.sponsorshipA.A. acknowledges partial support from the FWF (project "Quantum Transport Equations: Kinetic, Relativistic, and Diffusive Phenomena" and Wissenschaftskolleg "Differentialgleichungen"), the OAD (Amadeus project). I.M.G. is supported by NSF-DMS 0807712. M.P.G. is supported by NSF-DMS-1109682. C.M. would like to thank Cambridge University for providing repeated hospitality in 2009, thanks to the Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST). Support from the Institute of Computational Engineering and Sciences at the University of Texas at Austin is also gratefully acknowledged.
dc.publisherWorld Scientific Pub Co Pte Lt
dc.subjectFokkerPlanck operator
dc.subjectlarge-time behavior
dc.subjectspectral gap
dc.subjectstationary solution
dc.subjectWigner transform
dc.titleTHE WIGNER–FOKKER–PLANCK EQUATION: STATIONARY STATES AND LARGE TIME BEHAVIOR
dc.typeArticle
dc.identifier.journalMathematical Models and Methods in Applied Sciences
dc.contributor.institutionTechnische Universitat Wien, Vienna, Austria
dc.contributor.institutionUniversity of Texas at Austin, Austin, United States
dc.contributor.institutionCentre de Recherche en Mathematiques de la Decision, Paris, France
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdom
dc.contributor.institutionUniversity of Illinois at Chicago, Chicago, United States
dc.date.published-online2012-09-10
dc.date.published-print2012-11


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