A First-Passage Time Approach to Diffusion in Liquids and Superionic Conductors

Abstract

As a new tool to investigate single-particle motion in condensed matter, a first-passage time (FPT) approach to diffusion is developed and applied to the molecular dynamics simulations of simple liquids and superionic conductor CaF₂. It is shown that a continuous diffusion model reproduces the observed FPT distribution quite well for both liquids and CaF₂, which enables us to evaluate diffusion constants with good accuracy by our method. On a length scale as small as a lattice constant, however, the effect of hopping appears in the FPT distribution of F^? ions, which can not be described by a continuous diffusion model. A simple hopping diffusion model is proposed and examined from the FPT viewpoint.