A matrix form solution of the multi-dimensional generalized Langevin equation in the quadratic potential
Year: 2024
Type: article
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.
Authors: Mushtaq, Rana Imran, Wang, Chunyang, Zhi, Shichao, Zhao, Zengxuan, Malamula, Jeolous Nyasulu
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409920299