(joint work with I.M. Gamba, M.P. Gualdani, C. Sparber)
Dissipative open quantum systems like the quantum-Fokker-Planck (QFP) model are important for quantum Brownian motion and numerical simulations of nano-semiconductor devices. The evolution equation can be written in the Wigner phase-space framework or equaivalently for density matrix operators.
We discuss global-in-time wellposedness of the nonlinear QFP-Poisson model using density matrices, steady states of the linear QFP equation in a given confinement potential in the Wigner framework, and establish large-time convergence (with an exponential rate).
A. Arnold, I.M. Gamba, M.P. Gualdani, C. Sparber: The Wigner-Fokker-Planck Equation: Stationary States and Large Time Behavior, submitted, 2007.
A. Arnold, C. Sparber: Quantum dynamical semigroups for diffusion models with Hartree interaction, Comm. Math. Phys. 251, no.1 (2004) 179-207.