2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172016In this article we try to bridge the gap between the quantum dynamical semigroup and Wigner function approaches to quantum open systems. In particular we study stationary states and the long time asymptotics for the quantum Fokker-Planck equation. Our new results apply to open quantum systems in a harmonic confinement potential, perturbed by a (large) sub-quadratic term.19 pages, corrected typos and quoted Theorem 6 more preciselyMathematical PhysicsAnalysis of PDEs82C31; 81S25, 81S30text