  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.
