Geometric ergodicity of two-dimensional hamiltonian systems with a Lennard-Jones-like repulsive potential
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.
Cooke, B; Herzog, DP; Mattingly, JC; Mckinle, SA; Schmidler, SC
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