On the periodic Wigner--Poisson--Fokker--Planck system
The aim of this paper is the analysis of the coupled Wigner-Poisson-Fokker-Planck (WPFP) system in one dimension with periodic boundary conditions in the spatial direction. The existence and uniqueness of global classical solutions is analyzed. The main technical difficulty in the existence proof is to show that the quantum Fokker-Planck term is a semigroup-generator in a weighted \(L^2\)-space. The potential term is then a Lipschitz perturbation of it.
scientific article; zbMATH DE number 1866683