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Quantum dynamical semigroups for diffusion models with Hartree interaction

Anton Arnold·Christof Sparber
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Abstract

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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Anton Arnold, Christof Sparber. 2004-04-29. Quantum dynamical semigroups for diffusion models with Hartree interaction. https://doi.org/10.1007/s00220-004-1172-x

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