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• W1610060947 abstract "Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator AD in a Hilbert space H is used to describe an open quantum system. In this case the minimal self-adjoint dilation e K of AD can be regarded as the Hamiltonian of a closed system which contains the open system {AD, H}, but since e K is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family {A(µ)} of maximal dissipative operators depending on energy µ, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single Pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative" @default.
• W1610060947 created "2016-06-24" @default.
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• W1610060947 date "2006-10-31" @default.
• W1610060947 modified "2023-09-27" @default.
• W1610060947 title "Scattering Theory for Open Quantum Systems" @default.
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