The Wigner-Poisson-Fokker-Planck system: global-in-time solution and dispersive estimates

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dc.creatorArnold, Anton
dc.creatorDhamo, Elidon
dc.creatorManzini, Chiara
dc.date2005-05-18
dc.date.accessioned2026-07-07T05:20:00Z
dc.date.available2026-07-07T05:20:00Z
dc.descriptionThis paper is concerned with the Wigner-Poisson-Fokker-Planck system, a kinetic evolution equation for an open quantum system with a non-linear Hartree potential. Existence, uniqueness and regularity of global solutions to the Cauchy problem in 3 dimensions are established. The analysis is carried out in a weighted L^2-space, such that the linear quantum Fokker-Planck operator generates a dissipative semigroup.The non-linear potential can be controled by using the parabolic regularization of the system. The main technical difficulty for establishing global-in-time solutions is to derive a-priori estimates on the electric field:Inspired by a strategy for the classical Vlasov-Fokker-Planck equation, we exploit dispersive effects of the free transport operator. As a ``by-product'' we also derive a new a-priori estimate on the field in the Wigner-Poisson equation.
dc.identifierhttps://arxiv.org/abs/math/0505385
dc.identifierhttp://arxiv.org/abs/math/0505385
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75232
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subject35A05, 35K55, 35Q40, 47B44, 81Q99, 81S30, 82D37
dc.titleThe Wigner-Poisson-Fokker-Planck system: global-in-time solution and dispersive estimates
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