Document Type : Original Article
Authors
1 Ludong University
2 Institute of Theoretical Physics, School of Physics and Optoelectric Engineering, Ludong University, Yantai 264025, China
3 Institute of Theoretical Physics, School of Physics and Optoelectric Engineering, Ludong University
Abstract
In this research paper, we present an exact analytical solution of the multi-dimensional generalized Langevin equation with quadratic potentials. Our investigation provides detailed expressions for the two-dimensional probability distribution p(x1 , x2) 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)
- Mult-dimensional dynamics
- Analytical solution
- Laplace transformation
- Stochastic processes
Main Subjects
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