Activated rate processes in many dimensions: energy diffusion with slow adjustment of a nonreactive mode

Activated rate processes in two dimensions are studied analytically under the condition of weak friction on the reactive mode (energy diffusion) and high friction on the nonreactive coordinate. It is found that the process scenario and, as a consequence, the escape kinetics crucially depend on the strength of the mode coupling. When the coupling is strong the energy diffusion does not manifest itself. The kinetics is single-exponential with a rate constant independent of the friction on the reactive mode. For moderate mode coupling the energy diffusion plays an important role. Different process scenarios and, hence, the kinetics can be realized depending on the strength of friction on the both modes. Both multiexponential decay and single-exponential kinetics are possible. The latter may take place either when particles escape via the saddle on the potential surface (the traditional escape scenario) or when particles escape on a path that avoids the saddle point.