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Overdamped limit of generalized stochastic Hamiltonian systems for singular interaction potentials.
- Source :
- Journal of Evolution Equations; Jun2020, Vol. 20 Issue 2, p577-605, 29p
- Publication Year :
- 2020
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14243199
- Volume :
- 20
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Journal of Evolution Equations
- Publication Type :
- Academic Journal
- Accession number :
- 143492840
- Full Text :
- https://doi.org/10.1007/s00028-019-00530-8