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High-Order Adiabatic Approximation for Non-Hermitian Quantum System and Complexization of Berry's Phase

Chang-Pu Sun
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Abstract

In this paper the evolution of a quantum system drived by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation(HOAA) method with Berry's phase ,which is valid for either the Hermitian or the non-Hermitian cases. This method can be regarded as a non-trivial generalization of the HOAA method for closed quantum system presented by this author before. In a general situation, the probabilities of adiabatic decay and non-adiabatic transitions are explicitly obtained for the evolution of the non-Hermitian quantum system. It is also shown that the non-Hermitian analog of the Berry's phase factor for the non-Hermitian case just enjoys the holonomy structure of the dual linear bundle over the parameter manifold. The non-Hermitian evolution of the generalized forced harmonic oscillator is discussed as an illustrative examples.

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Chang-Pu Sun. 1993-05-02. High-Order Adiabatic Approximation for Non-Hermitian Quantum System and Complexization of Berry's Phase. https://doi.org/10.1088/0031-8949%2F48%2F4%2F002

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