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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.23385 |
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Table of 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.