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

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.

13 pages. to appear in Comm. Math. Sci