Communications in Mathematical Sciences

Volume 5 (2007)

Number 4

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

Pages: 765 – 777

DOI: http://dx.doi.org/10.4310/CMS.2007.v5.n4.a1

Authors

Lukas Neumann

Christof Sparber

Abstract

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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