Theory of non-stationary activated rate processes : nonexponential relaxation kinetics

TL;DR

This paper develops a microscopic model for non-stationary activated rate processes, revealing non-exponential relaxation kinetics and non-Markovian effects through analytical calculations of barrier dynamics and reaction rates.

Contribution

It introduces a novel analytical framework for non-stationary activated processes with a non-equilibrium bath, capturing non-exponential kinetics and non-Markovian effects.

Findings

Derived closed-form expressions for non-stationary Kramers rate.

Demonstrated strong dependence of reaction kinetics on bath relaxation.

Identified non-exponential relaxation as a hallmark of non-Markovian dynamics.

Abstract

We have explored a simple microscopic model to simulate a thermally activated rate process where the associated bath which comprises a set of relaxing modes is not in an equilibrium state. The model captures some of the essential features of non-Markovian Langevin dynamics with a fluctuating barrier. Making use of the Fokker-Planck description we calculate the barrier dynamics in the steady state and non-stationary regimes. The Kramers-Grote-Hynes reactive frequency has been computed in closed form in the steady state to illustrate the strong dependence of the dynamic coupling of the system with the relaxing modes. The influence of nonequilibrium excitation of the bath modes and its relaxation on the kinetics of activation of the system mode is demonstrated. We derive the dressed time-dependent Kramers rate in the nonstationary regime in closed analytical form which exhibits strong non-exponential relaxation kinetics of the reaction co-ordinate. The feature can be identified as a typical non-Markovian dynamical effect.