A Closed-Form Approach to Oscillatory Integrals in Level-Crossing Physics
Mathematical Physics
2025-07-01 v1 math.MP
Abstract
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.
Cite
@article{arxiv.2506.23385,
title = {A Closed-Form Approach to Oscillatory Integrals in Level-Crossing Physics},
author = {Maseim B. Kenmoe and Anicet D. Kammogne},
journal= {arXiv preprint arXiv:2506.23385},
year = {2025}
}