47E05 Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47)
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Year of publication
- 2008 (4)
Language
- English (4)
Keywords
- carrier and current densities (3)
- dissipative Schroedinger-type operators (3)
- characteristic function (2)
- density matrices (2)
- dissipative Schroedinger-Poisson systems (2)
- Sturm-Liouville operators (1)
- a priori estimates (1)
- delta perturbation (1)
- density matrix (1)
- dilation (1)
- dissipative Schroedinger operator (1)
- eigenfunction expansion (1)
- generalized eigenfunctions (1)
- minimal dilation (1)
- open quantum system (1)
- scattering theory (1)
- smooth operators (1)
Project
- D4 (4)
Application Area
- D (4)
We study in detail Schroedinger-type operators on a bounded interval of the real axis with dissipative boundary conditions. The characteristic function of such operators is computed, its minimal self-adjoint dilation is constructed and the generalized eigenfunction expansion for the dilation is developed. The problem is motivated by semiconductor physics.
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.