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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2506.23385 |
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| _version_ | 1866916816853401600 |
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| author | Kenmoe, Maseim B. Kammogne, Anicet D. |
| author_facet | Kenmoe, Maseim B. Kammogne, Anicet D. |
| contents | We present a closed-form, exact analytical solution, valid at finite times, to a class of multiple integrals with highly oscillatory kernels. Our approach leverages the intimate connection between these integrals and the minimal level-crossing model, namely the Landau-Zener model. Benchmarking against data from numerical simulations demonstrates excellent agreement validating our analytical method. Impacts of our results in level-crossing dynamics are also discussed. A dedicated Mathematica package named {\bf OscillatoryIntegralAnalytical.wl} publicly accessible in our \href{https://github.com/Kenmax15/Closed-Form-Approach-to-Oscillatory-Integrals/tree/main}{GitHub repository} allows generating the integrals for arbitrary order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23385 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Closed-Form Approach to Oscillatory Integrals in Level-Crossing Physics Kenmoe, Maseim B. Kammogne, Anicet D. Mathematical Physics We present a closed-form, exact analytical solution, valid at finite times, to a class of multiple integrals with highly oscillatory kernels. Our approach leverages the intimate connection between these integrals and the minimal level-crossing model, namely the Landau-Zener model. Benchmarking against data from numerical simulations demonstrates excellent agreement validating our analytical method. Impacts of our results in level-crossing dynamics are also discussed. A dedicated Mathematica package named {\bf OscillatoryIntegralAnalytical.wl} publicly accessible in our \href{https://github.com/Kenmax15/Closed-Form-Approach-to-Oscillatory-Integrals/tree/main}{GitHub repository} allows generating the integrals for arbitrary order. |
| title | A Closed-Form Approach to Oscillatory Integrals in Level-Crossing Physics |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2506.23385 |