The Wigner-Fokker-Planck equation: Stationary states and large time behavior - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2012

The Wigner-Fokker-Planck equation: Stationary states and large time behavior

Résumé

We consider the linear Wigner-Fokker-Planck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential. For a certain class of perturbations we prove that the equation admits a unique stationary solution in a weighted Sobolev space. A key ingredient of the proof is a new result on the existence of spectral gaps for Fokker-Planck type operators in certain weighted $L^2$--spaces. In addition we show that the steady state corresponds to a positive density matrix operator with unit trace and that the solutions of the time-dependent problem converge towards the steady state with an exponential rate.
Fichier principal
Vignette du fichier
1010.2791v1.pdf (319.35 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00526815 , version 1 (15-10-2010)

Identifiants

Citer

Anton Arnold, Irene Gamba, Maria Pia Gualdani, Stéphane Mischler, Clément Mouhot, et al.. The Wigner-Fokker-Planck equation: Stationary states and large time behavior. Mathematical Models and Methods in Applied Sciences, 2012, 22 (11), pp.1250034. ⟨10.1142/S0218202512500340⟩. ⟨hal-00526815⟩
485 Consultations
352 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More