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Springer Verlag, Monatshefte für Mathematik, 3(141), p. 237-257

DOI: 10.1007/s00605-003-0043-4

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On the Long-Time Behavior of the Quantum Fokker-Planck Equation

Journal article published in 2004 by J. A. Carrillo ORCID, Jean Dolbeault ORCID, Christof Sparber, P. A. Markowich
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This paper is available in a repository.

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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.