The adiabatic theorem for non-Hermitian quantum systems with real eigenvalues and the complex geometric phase
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914368442073088 |
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| author | Huang, Minyi Lee, Ray-Kuang |
| author_facet | Huang, Minyi Lee, Ray-Kuang |
| contents | 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 Grönwall 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 in non-Hermitian systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00968 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The adiabatic theorem for non-Hermitian quantum systems with real eigenvalues and the complex geometric phase Huang, Minyi Lee, Ray-Kuang Quantum Physics Mathematical Physics 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 Grönwall 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 in non-Hermitian systems. |
| title | The adiabatic theorem for non-Hermitian quantum systems with real eigenvalues and the complex geometric phase |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2511.00968 |