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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | https://arxiv.org/abs/2305.03637 |
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| _version_ | 1866910366418599936 |
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| author | Duong, Manh Hong Nguyen, Hung D. |
| author_facet | Duong, Manh Hong Nguyen, Hung D. |
| contents | We consider a system of interacting particles governed by the generalized Langevin equation (GLE) in the presence of external confining potentials, singular repulsive forces, as well as memory kernels. Using a Mori-Zwanzig approach, we represent the system by a class of Markovian dynamics. Under a general set of conditions on the nonlinearities, we study the large-time asymptotics of the multi-particle Markovian GLEs. We show that the system is always exponentially attractive toward the unique invariant Gibbs probability measure. The proof relies on a novel construction of Lyapunov functions. We then establish the validity of the small mass approximation for the solutions by an appropriate equation on any finite-time window. Important examples of singular potentials in our results include the Lennard-Jones and Coulomb functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_03637 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic analysis for the generalized Langevin equation with singular potentials Duong, Manh Hong Nguyen, Hung D. Probability Mathematical Physics We consider a system of interacting particles governed by the generalized Langevin equation (GLE) in the presence of external confining potentials, singular repulsive forces, as well as memory kernels. Using a Mori-Zwanzig approach, we represent the system by a class of Markovian dynamics. Under a general set of conditions on the nonlinearities, we study the large-time asymptotics of the multi-particle Markovian GLEs. We show that the system is always exponentially attractive toward the unique invariant Gibbs probability measure. The proof relies on a novel construction of Lyapunov functions. We then establish the validity of the small mass approximation for the solutions by an appropriate equation on any finite-time window. Important examples of singular potentials in our results include the Lennard-Jones and Coulomb functions. |
| title | Asymptotic analysis for the generalized Langevin equation with singular potentials |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2305.03637 |