Dissipative Schrödinger-type operator as a model for generation and recombination
Please always quote using this URN:urn:nbn:de:0296-matheon-4507
- Non-selfadjoint operators play an important role in the modeling of open quantum systems. We consider a one-dimensional Schroedinger-type operator with dissipative boundary conditions and dissipative delta potentials. An explicit description of the characteristic function, the minimal dilation and the generalized eigenfunctions of the dilation is given. The quantities of carrier and current densities are rigorously defined. Furthermore we will show that the current is not constant and that the variation of the current depend essentially on the chosen density matrix and imaginary parts of the delta potentials. This correspondence can be used to model a recombination-generation rate in the open quantum system.
Author: | Michael Baro, Hagen Neidhardt |
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URN: | urn:nbn:de:0296-matheon-4507 |
Referee: | Alexander Mielke |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2008/02/19 |
Release Date: | 2008/01/02 |
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Institute: | Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) |
MSC-Classification: | 47-XX OPERATOR THEORY / 47Axx General theory of linear operators / 47A20 Dilations, extensions, compressions |
47-XX OPERATOR THEORY / 47Axx General theory of linear operators / 47A55 Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] | |
47-XX OPERATOR THEORY / 47Bxx Special classes of linear operators / 47B44 Accretive operators, dissipative operators, etc. | |
47-XX OPERATOR THEORY / 47Exx Ordinary differential operators [See also 34Bxx, 34Lxx] / 47E05 Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47) | |
Preprint Number: | 438 |