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arXiv · 2511.19443

A matrix form solution of the multi-dimensional generalized Langevin equation in the quadratic potential

Rana Imran Mushtaq·Chunyang Wang·Shi Zhi·Zengxuan Zhao·J M Nyasulu
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Abstract

In this research paper, we present an exact matrix form analytical solution of the multi-dimensional generalized Langevin equation with quadratic potentials. Our investigation provides detailed expressions for the two-dimensional probability distribution and extends the understanding of the dynamics governed by harmonic potentials. By utilizing the inverse Laplace transformation, we offer a precise method to solve these equations, corroborated by specific examples. This study contributes to the fundamental understanding of stochastic processes in multi-dimensional systems with harmonic potentials and clarifies the limitations of our approach. While the findings are specific to quadratic potentials, they provide a robust framework for exploring related phenomena within this context.

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BibTeXRIS

Rana Imran Mushtaq, Chunyang Wang, Shi Zhi, Zengxuan Zhao, J M Nyasulu. 2025-11-15. A matrix form solution of the multi-dimensional generalized Langevin equation in the quadratic potential. https://doi.org/10.47176/ijpr.24.3.41887

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