On the Long-Time Behavior of the Quantum Fokker-Planck Equation |
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Authors: | C. Sparber J. A. Carrillo J. Dolbeault P. A. Markowich |
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Affiliation: | (1) Universität Wien, Austria;(2) Universidad Autonoma de Barcelona, Spain;(3) Université de Paris IX-Dauphine, France |
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Abstract: | We analyze the long-time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type diffusion operator, subject to confining potentials of harmonic oscillator type. We establish the existence and uniqueness of a non-equilibrium steady state for the corresponding dynamics. Further, using a (classical) convex Sobolev inequality, we prove an optimal exponential rate of decay towards this state and additionally give precise dispersion estimates in those cases, where no stationary state exists. |
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Keywords: | 2000 Mathematics Subject Classification: 35Q40 35B40 35K57 |
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