Renormalization Group for Barrier Escape: Crossover to Intermittency

We develop a critical theory of barrier crossing in overdamped systems with low barriers. Traditional calculations in reaction-rate theory typically assume the energy barrier separating two metastable states is much larger than the thermal energy of particles in the system. When the barrier vanishes, however, there is a qualitative change in behavior as the metastable states merge. Instead of escaping over a barrier, particles now slide down a sloping potential. We formulate a simple renormalization group description of this transition and derive the scaling form for the mean escape time with an arbitrary potential and spatially dependent noise. The renormalization group analysis unifies barrier crossing problems with the theory of intermittency, originally used to describe bursts of chaotic dynamics in discrete maps. This correspondence leads to an exact functional expression for the escape time that, in certain limits, recovers the results predicted by reaction-rate theory, intermittency theory, and deterministic dynamics.