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- Title
Asymptotic Analysis for the Generalized Langevin Equation with Singular Potentials.
- Authors
Duong, Manh Hong; Nguyen, Hung Dang
- 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.
- Publication
Journal of Nonlinear Science, 2024, Vol 34, Issue 4, p1
- ISSN
0938-8974
- Publication type
Article
- DOI
10.1007/s00332-024-10027-5