Renormalization Group for Barrier Escape: Crossover to Intermittency

Barrier crossing calculations in reaction-rate theory typically assume a large barrier limit. When the barrier vanishes, however, there is a qualitative change in behavior. Instead of crossing a barrier, particles slide down a sloping potential. We formulate a renormalization group description of this transition and derive the universal scaling behavior of the escape time in overdamped systems. Our critical theory unifies barrier crossing with intermittency theory for chaotic dynamics in discrete maps, and gives an analytical expression for the escape time valid for all barrier heights.