Brownian dynamics simulations of two-dimensional model for hopping times

Brownian dynamics simulations are used to study the mean first passage time for a hard disk diffusing in a channel. The disk has to hop pass another disk with the same diameter sigma but fixed in contact with the wall. This mean first passage time is expected to diverge with an exponent eta as the channel width (2R(p)) approaches that of the nonpassing limit (2sigma) for one disk to hop pass another. Our one disk model is similar to a disk diffusing in a two-dimensional container, shaped as a simplified configuration space of two passing disks in a flat channel of Kalinay. The Kalinay model was proposed recently to elucidate the disagreements between two different theoretical predictions for the exponent eta of the two disk hopping time divergences. For the one disk model, simple transition state theory and a Fick-Jacobs type of dimensional reduction approach predict exponents of 1 and 12, respectively. Our Brownian dynamics simulation, results are consistent with a value of 1.