Quantum dynamical semigroups for diffusion models with Hartree interaction

Details Quantum dynamical semigroups for diffusion models with Hartree interaction Quantum dynamical semigroups for diffusion models with Hartree interaction

2003-09-23

arxiv.org/abs/math-ph/0309052v2

Physics

Mathematical Physics

30 pages; Introduction changed, title changed, easier and shorter proofs due to new energy norm. to appear in Comm. Math. Phys

Scientific paper

10.1007/s00220-004-1172-x

We consider a class of evolution equations in Lindblad form, which model the dynamics of dissipative quantum mechanical systems with mean-field interaction. Particularly, this class includes the so-called Quantum Fokker-Planck-Poisson model. The existence and uniqueness of global-in-time, mass preserving solutions is proved, thus establishing the existence of a nonlinear conservative quantum dynamical semigroup. The mathematical difficulties stem from combining an unbounded Lindblad generator with the Hartree nonlinearity.

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