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 the temperature. 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 noisy saddle-node transition. We derive the universal scaling behavior and corrections to scaling for the mean escape time in overdamped systems with arbitrary barrier height. We also develop an accurate approximation to the full distribution of barrier escape times by approximating the eigenvalues of the Fokker-Plank operator as equally spaced. This lets us derive a family of distributions that captures the barrier crossing times for arbitrary barrier height. Our critical theory draws links between barrier crossing in chemistry, the renormalization group, and bifurcation theory.

Automated summary

This study discusses calculations of barrier crossing in chemical reaction-rate theory, stating that particles typically cross a barrier when the barrier is larger than the temperature. However, when the barrier disappears, particles slide down a sloping potential instead. The authors propose a renormalization group description of this noisy saddle-node transition and derive universal scaling behavior and corrections to scaling for mean escape time in overdamped systems. They also develop an accurate approximation to the full distribution of barrier escape times by approximating the eigenvalues of the Fokker-Plank operator as equally spaced.