Geometric Ergodicity of Two--dimensional Hamiltonian systems with a Lennard--Jones--like Repulsive Potential

Ben Cooke; David P. Herzog; Jonathan C. Mattingly; Scott A. McKinley; Scott C. Schmidler

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arXiv · 1104.3842

Geometric Ergodicity of Two--dimensional Hamiltonian systems with a Lennard--Jones--like Repulsive Potential

Ben Cooke·David P. Herzog·Jonathan C. Mattingly·Scott A. McKinley·Scott C. Schmidler

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Abstract

In this paper we establish the ergodicity of Langevin dynamics for simple two-particle system involving a Lennard-Jones type potential. To the best of our knowledge, this is the first such result for a system operating under this type of potential. Moreover we show that the dynamics are {\it geometrically} ergodic (have a spectral gap) and converge at a geometric rate. Methods from stochastic averaging are used to establish the existence of a Lyapunov function. The existence of a Lyapunov function in this setting seems resistant to more traditional approaches. This is a corrected version of the article.

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BibTeX RIS

Ben Cooke, David P. Herzog, Jonathan C. Mattingly, Scott A. McKinley, Scott C. Schmidler. 2011-04-19. Geometric Ergodicity of Two--dimensional Hamiltonian systems with a Lennard--Jones--like Repulsive Potential. https://arxiv.org/abs/1104.3842

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