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

C. Sparber·J. A. Carrillo·J. Dolbeault·P. A. Markowich
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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 scattering operator, subject to confining potentials of harmonic oscillator type. We establish the conditions under which there exists a thermal equilibrium state and prove exponential decay towards it, using (classical) entropy-methods. Additionally, we give precise dispersion estimates in the cases were no equilibrium state exists.

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C. Sparber, J. A. Carrillo, J. Dolbeault, P. A. Markowich. 2002-04-16. On the Long Time Behavior of the Quantum Fokker-Planck equation. https://arxiv.org/abs/math-ph/0204032

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