Soluble stochastic dynamics of quasi-one-dimensional single-file fluid self-diffusion

Abstract

We solve a model of random-walk stochastic dynamics for hard single-file fluids in the experimentally important quasi-one-dimensional regime. This is a nontrivial extension of exact solution beyond one dimension. We point out that quasi-one-dimensional single-file self-diffusion of one-component hard fluids of diameter a under stochastic forces is equivalent at long time to a one-dimensional hard-rod fluid with the same linear density but a different diameter, a(eff). This effective diameter is controlled by the details of the relative dynamics between the transverse and longitudinal directions. There are two regimes of limiting behavior. For very fast transverse motion, the system is likely (but we cannot prove rigorously) to be equivalent to the soluble-oriented hard-rectangle or cylinder systems, with a(eff)=a. With very slow transverse motion, the self-diffusion dynamics is described by an equivalent soluble one-dimensional mixture of fluids with a(eff)=a(ave), the average longitudinal separation between nearest-neighbor particles at contact. We have explored our theoretical predictions with Monte Carlo simulations.