Reaction rates and the noisy saddle-node bifurcation: Renormalization group for barrier crossing

Barrier crossing calculations in chemical reaction-rate theory typically assume that the barrier is large compared to temperature. When vanishes, however, there a qualitative change behavior. Instead of barrier, particles slide down sloping potential. We formulate renormalization group description this noisy saddle-node transition. derive universal scaling behavior and corrections for mean escape time overdamped systems with arbitrary height. also develop an accurate approximation full distribution times by approximating eigenvalues Fokker-Plank operator as equally spaced. This lets us family distributions captures Our critical draws links between chemistry, group, bifurcation theory.