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- Publisher
- Springer Journals
- Copyright
- Copyright © 2010 by Springer Basel AG
- Subject
- Mathematics; Analysis
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-010-0064-0
- Publisher site
- See Article on Publisher Site
Abstract
We construct N -particle Langevin dynamics in $${\mathbb{R}^d}$$ or in a cuboid region with periodic boundary for a wide class of N -particle potentials Φ and initial distributions which are absolutely continuous w.r.t. Lebesgue measure. The potentials are in particular allowed to have singularities and discontinuous gradients (forces). An important point is to prove an L p -uniqueness of the associated non-symmetric, non-sectorial degenerate elliptic generator. Analyzing the associated functional analytic objects, we also give results on the long-time behaviour of the dynamics, when the invariant measure is finite: Firstly, we prove the weak mixing property whenever it makes sense (i.e. whenever {Φ < ∞} is connected). Secondly, for a still quite large class of potentials we also give a rate of convergence of time averages to equilibrium when starting in the equilibrium distribution. In particular, all results apply to N -particle systems with pair interactions of Lennard–Jones type.
Journal
Journal of Evolution Equations – Springer Journals
Published: Aug 1, 2010