A Closed-Form Approach to Oscillatory Integrals in Level-Crossing Physics

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Detalles Bibliográficos
Autores principales:	Kenmoe, Maseim B., Kammogne, Anicet D.
Formato:	Preprint
Publicado:	2025
Materias:	Mathematical Physics
Acceso en línea:	Acceder al recurso
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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

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