
On the Long-Time Behavior of the Quantum Fokker-Planck Equation
Carrillo, José A.; Dolbeault, Jean; Markowich, Peter; Sparber, Christof (2004), On the Long-Time Behavior of the Quantum Fokker-Planck Equation, Monatshefte für Mathematik, 141, 3, p. 237-257. http://dx.doi.org/10.1007/s00605-003-0043-4
Type
Article accepté pour publication ou publiéDate
2004Journal name
Monatshefte für MathematikVolume
141Number
3Publisher
Springer
Pages
237-257
Publication identifier
Metadata
Show full item recordAuthor(s)
Carrillo, José A.Dolbeault, Jean

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Markowich, Peter
Sparber, Christof
Abstract (EN)
We analyze the long-time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type diffusion operator, subject to confining potentials of harmonic oscillator type. We establish the existence and uniqueness of a non-equilibrium steady state for the corresponding dynamics. Further, using a (classical) convex Sobolev inequality, we prove an optimal exponential rate of decay towards this state and additionally give precise dispersion estimates in those cases, where no stationary state exists.Subjects / Keywords
Open quantum system; Lindblad condition; Wigner transform; Fokker-Planck operator; long-time asymptotic; logarithmic Sobolev inequalityRelated items
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