The adiabatic theorem for non-Hermitian quantum systems with real eigenvalues and the complex geometric phase

Minyi Huang; Ray-Kuang Lee

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arXiv · 2511.00968

The adiabatic theorem for non-Hermitian quantum systems with real eigenvalues and the complex geometric phase

Minyi Huang·Ray-Kuang Lee

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Abstract

The adiabatic theorem is one of the most interesting and significant theorems in quantum mechanics. However, the adiabatic theorem can fail for general non-Hermitian quantum systems. In this paper, by utilizing the complex geometric phase, the functional calculus for biorthogonal systems and the Gr\"{o}nwall inequality, we prove rigorously that the adiabatic theorem is still valid for diagonalizable non-Hermitian systems with real eigenvalues. The proof also justifies the definition of a complex Berry phase for non-Hermitian systems, in both Abelian and non-Abelian cases.

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Minyi Huang, Ray-Kuang Lee. 2025-11-02. The adiabatic theorem for non-Hermitian quantum systems with real eigenvalues and the complex geometric phase. https://arxiv.org/abs/2511.00968

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