Nontrivial eigenvalues of the Liouvillian of an open quantum system
| Autor: | Ruri Nakano, Tomio Petrosky, Naomichi Hatano |
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| Rok vydání: | 2010 |
| Předmět: |
Physics and Astronomy (miscellaneous)
Statistical Mechanics (cond-mat.stat-mech) General Mathematics FOS: Physical sciences Mathematics::Spectral Theory Integral equation Open quantum system symbols.namesake Quantum dot symbols Hamiltonian (quantum mechanics) Condensed Matter - Statistical Mechanics Eigenvalues and eigenvectors Mathematical physics Mathematics |
| DOI: | 10.48550/arxiv.1010.5302 |
| Popis: | We present methods of finding complex eigenvalues of the Liouvillian of an open quantum system. The goal is to find eigenvalues that cannot be predicted from the eigenvalues of the corresponding Hamiltonian. Our model is a T-type quantum dot with an infinitely long lead. We suggest the existence of the non-trivial eigenvalues of the Liouvillian in two ways: one way is to show that the original problem reduces to the problem of a two-particle Hamiltonian with a two-body interaction and the other way is to show that diagram expansion of the Green's function has correlation between the bra state and the ket state. We also introduce the integral equations equivalent to the original eigenvalue problem. Comment: 5 pages, 2 figures, proceedings |
| Databáze: | OpenAIRE |
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