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Abstract
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.
Original language | English |
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Article number | 62 |
Journal | Journal of Nonlinear Science |
Volume | 34 |
Issue number | 4 |
DOIs | |
Publication status | Published - 14 May 2024 |
Keywords
- 60H10
- Lyapunov functions
- Singular potentials
- Small mass limits
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Dive into the research topics of 'Asymptotic Analysis for the Generalized Langevin Equation with Singular Potentials'. Together they form a unique fingerprint.Projects
- 2 Finished
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Rigorous coarse-graining of defects at positive temperature
Duong, H. (Principal Investigator)
Engineering & Physical Science Research Council
1/06/22 → 31/05/23
Project: Research Councils
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Variational structures, convergence to equilibrium and multiscale analysis for non-Markovian systems
Duong, H. (Principal Investigator)
Engineering & Physical Science Research Council
1/02/22 → 30/06/24
Project: Research Councils