Nature of self-diffusion in two-dimensional fluids

TL;DR

This paper combines analytical and numerical methods to study self-diffusion in two-dimensional fluids, revealing asymptotic behaviors and finite-size effects that deepen understanding of anomalous diffusion.

Contribution

It provides the exact solution of the consistency equation in the thermodynamic limit and clarifies the large-time asymptotics of key diffusion quantities.

Findings

Velocity autocorrelation decays as 1/(t√ln t) with rescaled time

Kinematic viscosity approaches a finite non-zero value in the thermodynamic limit

Finite size effects on the diffusion coefficient are characterized

Abstract

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function using a consistency equation relating these quantities. We numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the velocity autocorrelation function. An asymptotic decay law of the velocity autocorrelation function resembles the previously known self-consistent form, $1/(t\sqrt{\ln t})$, however with a rescaled time.