Overdamped limit of generalized stochastic Hamiltonian systems for singular interaction potentials
Functional Analysis
2018-09-19 v1
Abstract
First weak solutions of generalized stochastic Hamiltonian systems (gsHs) are constructed via essential m-dissipativity of their generators on a suitable core. For a scaled gsHs we prove convergence of the corresponding semigroups and tightness of the weak solutions. This yields convergence in law of the scaled gsHs to a distorted Brownian motion. In particular, the results confirm the convergence of the Langevin dynamics in the overdamped regime to the overdamped Langevin equation. The proofs work for a large class of (singular) interaction potentials including, e.g., potentials of Lennard--Jones type.
Keywords
Cite
@article{arxiv.1809.06788,
title = {Overdamped limit of generalized stochastic Hamiltonian systems for singular interaction potentials},
author = {Andreas Nonnenmacher and Martin Grothaus},
journal= {arXiv preprint arXiv:1809.06788},
year = {2018}
}