Instantons and the Fluctuating Path Description of Reactions in Complex Environments

Abstract

The classical kinetic laws break down for fast barrier crossing events in slowly relaxing environments such as glasses, viscous fluids, and biomolecules. One approach to rate processes in a general fluctuating environment uses a path integral formalism. The population dynamics can be approximated using the steepest descent method which leads to a description with a distributed, time-varying rate coefficient. In certain situations, this method fails to describe the long time dynamics due to large amplitude fluctuations away from the dominant survival path. Paths transiently entering the high-rate regions can give significant contributions to the survival probability. These fluctuations are the analogue of instantons in the usual quantum tunneling problem. A frequency-dependent rate coefficient naturally emerges when instanton interactions are taken into account. When instanton interactions are ignored, the instanton contribution can restore the single-exponential decay law.