Nontrivial Eigenvalues of the Liouvillian of an Open Quantum System |
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Authors: | Ruri Nakano Naomichi Hatano and Tomio Petrosky |
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Institution: | (1) Jiangsu Laboratory of Advanced Functional Materials, and College of Physics and Engineering, Changshu Institute of Technology, 215500 Changshu, China; |
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Abstract: | 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. |
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Keywords: | |
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