نوع مقاله : مقاله پژوهشی
نویسندگان
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
چکیده
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.
کلیدواژهها
- Generalized Langevin equation (GLE)
- Mult-dimensional dynamics
- Analytical solution
- Laplace transformation
- Stochastic processes
موضوعات
عنوان مقاله [English]
A Matrix Form Solution of the Multi-dimensional Generalized Langevin Equation in the Quadratic Potential
نویسندگان [English]
- Rana Imran Mushtaq 1
- Chunyang Wang 2
- Shichao Zhi 3
- Zengxuan Zhao 3
- Jeolous Nyasulu Malamula 3
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
چکیده [English]
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.
کلیدواژهها [English]
- Generalized Langevin equation (GLE)
- Mult-dimensional dynamics
- Analytical solution
- Laplace transformation
- Stochastic processes
)