Exact-WKB Analysis of Two-level Floquet Systems
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912669381951488 |
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| author | Fujimori, Toshiaki Kamata, Syo Misumi, Tatsuhiro Sueishi, Naohisa Taya, Hidetoshi |
| author_facet | Fujimori, Toshiaki Kamata, Syo Misumi, Tatsuhiro Sueishi, Naohisa Taya, Hidetoshi |
| contents | We explore the application of the exact Wentzel-Kramers-Brillouin (WKB) analysis to two-level Floquet systems and establish a systematic procedure to calculate the quasi-energy and Floquet effective Hamiltonian. We show that, in the exact-WKB analysis, the quasi-energy and Floquet effective Hamiltonian can be expressed in terms of cycle integrals (Voros symbol), which characterize monodromy matrices for Schrödinger-type differential equations governing two-level Floquet systems. We analytically evaluate the cycle integrals using the low-frequency expansion and derive both perturbative and non-perturbative corrections to the quasi-energy and Floquet effective Hamiltonian. To verify the accuracy of our results, we compare them with numerical calculations and analyze resonant oscillations, which reveal non-perturbative features that cannot be captured by the perturbative expansion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_12838 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact-WKB Analysis of Two-level Floquet Systems Fujimori, Toshiaki Kamata, Syo Misumi, Tatsuhiro Sueishi, Naohisa Taya, Hidetoshi High Energy Physics - Phenomenology High Energy Physics - Theory We explore the application of the exact Wentzel-Kramers-Brillouin (WKB) analysis to two-level Floquet systems and establish a systematic procedure to calculate the quasi-energy and Floquet effective Hamiltonian. We show that, in the exact-WKB analysis, the quasi-energy and Floquet effective Hamiltonian can be expressed in terms of cycle integrals (Voros symbol), which characterize monodromy matrices for Schrödinger-type differential equations governing two-level Floquet systems. We analytically evaluate the cycle integrals using the low-frequency expansion and derive both perturbative and non-perturbative corrections to the quasi-energy and Floquet effective Hamiltonian. To verify the accuracy of our results, we compare them with numerical calculations and analyze resonant oscillations, which reveal non-perturbative features that cannot be captured by the perturbative expansion. |
| title | Exact-WKB Analysis of Two-level Floquet Systems |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2504.12838 |