Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation

TL;DR

This paper derives a generalized Einstein relation applicable to normal, sub-, and super-diffusive behaviors in two-dimensional fluids, and validates it through molecular dynamics simulations focusing on medium to high densities.

Contribution

It introduces a generalized asymptotic Einstein relation based on the Langevin equation that extends the classical relation to anomalous diffusion regimes.

Findings

Super-diffusive behavior observed at medium densities.

Normal diffusion identified at higher densities.

Potential transition to sub-diffusion at very high densities.

Abstract

Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.