A matrix form solution of the multi-dimensional generalized Langevin equation in the quadratic potential
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912727355621376 |
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| author | Mushtaq, Rana Imran Wang, Chunyang Zhi, Shi Zhao, Zengxuan Nyasulu, J M |
| author_facet | Mushtaq, Rana Imran Wang, Chunyang Zhi, Shi Zhao, Zengxuan Nyasulu, J M |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_19443 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A matrix form solution of the multi-dimensional generalized Langevin equation in the quadratic potential Mushtaq, Rana Imran Wang, Chunyang Zhi, Shi Zhao, Zengxuan Nyasulu, J M Statistical Mechanics Data Analysis, Statistics and Probability 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. |
| title | A matrix form solution of the multi-dimensional generalized Langevin equation in the quadratic potential |
| topic | Statistical Mechanics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2511.19443 |