Effects of Hydrodynamic Backflow on the Transmission Coefficient of a Barrier-Crossing Brownian Particle

The slow power law decay of the velocity autocorrelation function of a particle moving stochastically in a condensed-phase fluid is widely attributed to the momentum that fluid molecules displaced by the particle transfer back to it during the course of its motion. The forces created by this backflow effect are known as Basset forces, and they have been found in recent analytical work and numerical simulations to be implicated in a number of interesting dynamical phenomena, including boosted particle mobility in tilted washboard potentials. Motivated by these findings, the present paper is an investigation of the role of backflow in thermally activated barrier crossing, the governing process in essentially all condensed-phase chemical reactions. More specifically, it is an exact analytical calculation, carried out within the framework of the reactive-flux formalism, of the transmission coefficient κ(t) of a Brownian particle that crosses an inverted parabola under the influence of a colored noise process originating in the Basset force and a Markovian time-local friction. The calculation establishes that κ(t) is significantly enhanced over its backflow-free limit.