Stability of steady states in kinetic Fokker-Planck equations for Bosons and Fermions
Lukas Neumann, Christof Sparber
TL;DR
This paper investigates the stability of steady states in quantum kinetic Fokker-Planck equations for Bosons and Fermions, establishing existence and exponential convergence to equilibrium.
Contribution
It provides the first rigorous proof of existence and stability of solutions for these quantum kinetic equations in the perturbative regime.
Findings
Existence of classical solutions in the perturbative regime
Exponential convergence towards equilibrium states
Validation of quantum kinetic models 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.
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Taxonomy
TopicsGas Dynamics and Kinetic Theory · Advanced Thermodynamics and Statistical Mechanics · Cold Atom Physics and Bose-Einstein Condensates