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Open Quantum Systems Decoherence

The Wigner-Fokker-Planck equation: Stationary states and large-time behavior

arXiv
Authors: Anton Arnold, Irene M. Gamba, Maria Pia Gualdani, Stephane Mischler, Clement Mouhot, Christof Sparber

Year

2010

Paper ID

10866

Status

Preprint

Abstract Read

~2 min

Abstract Words

100

Citations

N/A

Abstract

We consider the linear Wigner-Fokker-Planck 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 Fokker-Planck type operators in certain weighted L2-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.

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  • This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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  • We consider the linear Wigner-Fokker-Planck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1010.2791 [2] arXiv https://arxiv.org/abs/1010.2791 [3] Publisher https://arxiv.org/abs/1010.2791

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