On the Long-Time Behavior of the Quantum Fokker-Planck Equation

C. Sparber*, J. A. Carrillo, J. Dolbeault, P. A. Markowich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)237-257
Number of pages21
JournalMonatshefte fur Mathematik
Issue number3
StatePublished - Mar 2004
Externally publishedYes


  • Fokker-Planck operator
  • Lindblad condition
  • Logarithmic Sobolev inequality
  • Long-time asymptotic
  • Open quantum system
  • Wigner transform

ASJC Scopus subject areas

  • General Mathematics


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