Calculating the hopping times of confined fluids: Two hard disks in a box

The dynamical transition between the anomalous single file diffusion of highly confined fluids and bulk normal diffusion can be described by a phenomenological model involving a particle hopping time τ _hop. We suggest a theoretical formalism that will be useful for the calculation of τ _hop for a variety of systems and test it using a simple model consisting of two hard disks confined to a rectangular box with hard walls. In the case where the particles are moving diffusively, we find the hopping time diverges as a power law in the threshold region with an exponent of -(3/2). Under conditions where the particles move inertially, transition state theory predicts a power law behavior with an exponent of -2. Molecular dynamics simulations confirm the transition state theory result for inertial dynamics, while Brownian dynamics simulations suggest the scaling exponent is highly sensitive to the details of the algorithm.