Scattering Theory for Open Quantum Systems

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dc.creatorBehrndt, J.
dc.creatorMalamud, M. M.
dc.creatorNeidhardt, H.
dc.date2006-10-31
dc.date.accessioned2026-07-07T07:28:31Z
dc.date.available2026-07-07T07:28:31Z
dc.descriptionQuantum 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 $A_D$ in a Hilbert space $\sH$ is used to describe an open quantum system. In this case the minimal self-adjoint dilation $\widetilde K$ of $A_D$ can be regarded as the Hamiltonian of a closed system which contains the open system $\{A_D,\sH\}$, but since $\widetilde K$ 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 and quantum transmitting Schrödinger-Poisson systems.
dc.identifierhttps://arxiv.org/abs/math-ph/0610088
dc.identifierhttp://arxiv.org/abs/math-ph/0610088
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117756
dc.subjectMathematical Physics
dc.subject47A40, 47A55, 47B25, 47B44, 47E05
dc.titleScattering Theory for Open Quantum Systems
dc.typetext

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