On the periodic Wigner–Poisson–Fokker–Planck system

This paper is concerned with the existence and uniqueness analysis of global classical solutions of a diffusive quantum evolution equation with nonlinear coupling to the Poisson equation. The main technical difficulty in the existence proof is to show that the quantum Fokker–Planck term is a semigroup-generator in a weighted L2-space. The potential term is then a Lipschitz perturbation of it.  2002 Elsevier Science (USA). All rights reserved.