Communications in Mathematical Sciences
Volume 15 (2017)
Geometric ergodicity of two-dimensional Hamiltonian systems with a Lennard–Jones-like repulsive potential
Pages: 1987 – 2025
We establish ergodicity of the Langevin dynamics for a simple two-particle system involving a Lennard–Jones type potential. Moreover, we show that the dynamics is geometrically ergodic; that is, the system converges to stationarity exponentially fast. Methods from stochastic averaging are used to establish the existence of the appropriate Lyapunov function.
Langevin dynamics, Lennard–Jones potential, geometric ergodicity, Lyapunov function, stochastic averaging
2010 Mathematics Subject Classification
37A25, 60H10, 82C31
Paper received on 21 April 2011.
Paper accepted on 1 July 2017.