| Autor: |
Boitsev, A. A., Brasche, J. F., Malamud, M. M., Neidhardt, H., Popov, I. Yu. |
| Rok vydání: |
2017 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s00023-018-0698-y |
| Popis: |
We consider symmetric operators of the form $S := A\otimes I_{\mathfrak T} + I_{\mathfrak H} \otimes T$ where $A$ is symmetric and $T = T^*$ is (in general) unbounded. Such operators naturally arise in problems of simulating point contacts to reservoirs. We construct a boundary triplet $\Pi_S$ for $S^*$ preserving the tensor structure. The corresponding $\gamma$-field and Weyl function are expressed by means of the $\gamma$-field and Weyl function corresponding to the boundary triplet $\Pi_A$ for $A^*$ and the spectral measure of $T$. Applications to 1-D Schr\"odinger and Dirac operators are given. A model of electron transport through a quantum dot assisted by cavity photons is proposed. In this model the boundary operator is chosen to be the well-known Jaynes-Cumming operator which is regarded as the Hamiltonian of the quantum dot. |
| Databáze: |
arXiv |
| Externí odkaz: |
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