Effect of Memory and Inertial Contribution on Transition-Time Distributions: Theory and Simulations

Transition paths refer to the time taken by molecules to cross a barrier separating two molecular conformations. In this work, we study how memory, as well as inertial contribution in the dynamics along a reaction coordinate, can affect the distribution of the transition-path time. We use a simple model of dynamics governed by a generalized Langevin equation with a power-law memory along with the inertial term, which was neglected in previous studies, where memory effects were explored only in the over-damped limit. We derive an approximate expression for the transit-time distribution and discuss our results for the short- and long-time limits and also compare it with known results in the high friction (overdamped) limit as well as in the Markovian limit. We have developed a numerical algorithm to test our theoretical results against extensive numerical simulations.

Automated summary

This study investigates the impact of memory and inertia on the distribution of transition-path time for molecules crossing a barrier between two molecular conformations. A simple model of dynamics governed by a generalized Langevin equation with a power-law memory and an inertial term is used. The approximate expression for the transit-time distribution is derived and verified through numerical simulations using a developed numerical algorithm.