Two-level adiabatic transition probability for small avoided crossings generated by tangential intersections
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914070879272960 |
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| author | Higuchi, Kenta Watanabe, Takuya |
| author_facet | Higuchi, Kenta Watanabe, Takuya |
| contents | In this paper, the asymptotic behaviors of the transition probability for two-level avoided crossings are studied under the limit where two parameters (adiabatic parameter and energy gap parameter) tend to zero. This is a continuation of our previous works where avoided crossings are generated by tangential intersections and obey a non-adiabatic regime. The main results elucidate not only the asymptotic expansion of transition probability but also a quantum interference caused by several avoided crossings and a coexistence of two-parameter regimes arising from different vanishing orders. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_17777 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-level adiabatic transition probability for small avoided crossings generated by tangential intersections Higuchi, Kenta Watanabe, Takuya Mathematical Physics Classical Analysis and ODEs Quantum Physics Primary 81Q20, Secondary 34E20, 35B40, 35Q40 In this paper, the asymptotic behaviors of the transition probability for two-level avoided crossings are studied under the limit where two parameters (adiabatic parameter and energy gap parameter) tend to zero. This is a continuation of our previous works where avoided crossings are generated by tangential intersections and obey a non-adiabatic regime. The main results elucidate not only the asymptotic expansion of transition probability but also a quantum interference caused by several avoided crossings and a coexistence of two-parameter regimes arising from different vanishing orders. |
| title | Two-level adiabatic transition probability for small avoided crossings generated by tangential intersections |
| topic | Mathematical Physics Classical Analysis and ODEs Quantum Physics Primary 81Q20, Secondary 34E20, 35B40, 35Q40 |
| url | https://arxiv.org/abs/2404.17777 |