Transition State Theory in a Solvable Model

Transition state theory is a method for calculating transition rates between metastable states in ergodic dynamical systems.In this method one counts the number of times a typical trajectory between one metastable set to the other crosses a given hypersurface that separates the states in phase space. This count gives the average rate of crossing the surface. In this talk I will present an analysis of the predictions of Transition state theory and its underlying assumptions in the context of the Kac-Zwanzig model. This model is a simplified system in which a 1D particle is coupled to a bath of harmonic oscillators.