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

Mushtaq, Rana Imran; Wang, Chunyang; Zhi, Shichao; Zhao, Zengxuan; Malamula, Jeolous Nyasulu

doi:10.47176/ijpr.24.3.41887

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

Document Type : Original Article

Authors

Rana Imran Mushtaq ¹

Chunyang Wang ²

Shichao Zhi ¹

Zengxuan Zhao ¹

Jeolous Nyasulu Malamula ¹

¹ Institute of Theoretical Physics, School of Physics and Optoelectric Engineering, Ludong University, Yantai 264025,China

² -Institute of Theoretical Physics, School of Physics and Optoelectric Engineering, Ludong University, Yantai 264025,China -Yantai Institute of Coastal Zone Research, Chinese Academy of Science, Yantai 264003, China

https://doi.org/10.47176/ijpr.24.3.41887

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.

Keywords

generalized Langevin equation (GLE)

multi-dimensional dynamics

analytical solution

Laplace transformation

stochastic processes

Subjects

Condensed Matter Physics

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