Abstract
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 language | English |
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Pages (from-to) | 237-257 |
Journal | Monatshefte fur Mathematik |
Volume | 141 |
DOIs | |
Publication status | Published - 1 Jan 2004 |
Keywords
- Fokker-Planck operator
- Lindblad condition
- Logarithmic Sobolev inequality
- Long-time asymptotic
- Open quantum system
- Wigner transform