Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
 
Abstract : We 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.
 
 
ON THE LONG TIME BEHAVIOR OF THE QUANTUM FOKKER-PLANCK EQUATION
CARRILLO José A., DOLBEAULT Jean, MARKOWICH Peter
SPARBER C.
2002-12
22-04-2002
 
Université de PARIS - DAUPHINE
Place du Maréchal de Lattre De Tassigny - 75775 PARIS CEDEX 16 - FRANCE
Téléphone : +33 (0)1 44-05-49-23 - fax : +33 (0)1 44-05-45-99