title: Calculating the hopping times of confined fluids: two hard disks in a box.
abstract: 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 tau(hop). We suggest a theoretical formalism that will be useful for the calculation of tau(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.
authors.affiliation: Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA. richard.bowles@usask.ca
authors.forename: R K
authors.initials: RK
authors.lastname: Bowles
authors.forename: K K
authors.initials: KK
authors.lastname: Mon
authors.forename: J K
authors.initials: JK
authors.lastname: Percus