Stability of steady states in kinetic Fokker-Planck equations for Bosons and Fermions

We study a class of nonlinear kinetic Fokker-Planck type equations modeling quantum particles which obey the Bose-Einstein and Fermi-Dirac statistics, respectively. We establish the existence of classical solutions in the perturbative regime and prove exponential convergence towards the equilibrium.

Keywords

Fokker-Planck operator, Bose-Einstein statistics, Fermi-Dirac statistics, long time behavior

2010 Mathematics Subject Classification

76R50, 82C10, 82C40, 82D37

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Published 1 January 2007