On the Long Time Behavior of the Quantum Fokker-Planck equation
Mathematical Physics
2007-05-23 v1 Analysis of PDEs
math.MP
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.
Keywords
Cite
@article{arxiv.math-ph/0204032,
title = {On the Long Time Behavior of the Quantum Fokker-Planck equation},
author = {C. Sparber and J. A. Carrillo and J. Dolbeault and P. A. Markowich},
journal= {arXiv preprint arXiv:math-ph/0204032},
year = {2007}
}