2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57044We analyze the long time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type scattering operator, subject to confining potentials of harmonic oscillator type. We establish the conditions under which there exists a thermal equilibrium state and prove exponential decay towards it, using (classical) entropy-methods. Additionally, we give precise dispersion estimates in the cases were no equilibrium state exists.Mathematical PhysicsAnalysis of PDEs47N50, 35K15, 46N55text