Simplified Self-Consistent Theory of Colloid Dynamics

TL;DR

This paper introduces a simplified version of the self-consistent generalized Langevin equation theory for colloid dynamics that omits short-time moment conditions, maintaining accuracy at intermediate and long times.

Contribution

A simplified SCGLE theory is proposed that removes the need for calculating exact short-time properties, simplifying application without losing accuracy at longer times.

Findings

Simplified theory matches original results at intermediate and long times.

Deviations occur only at short times and are negligible.

Comparison with model systems confirms the validity of the simplification.

Abstract

One of the main elements of the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics [Phys. Rev. E {\bf 62}, 3382 (2000); ibid {\bf 72}, 031107 (2005)] is the introduction of exact short-time moment conditions in its formulation. The need to previously calculate these exact short-time properties constitutes a practical barrier for its application. In this note we report that a simplified version of this theory, in which this short-time information is eliminated, leads to the same results in the intermediate and long-time regimes. Deviations are only observed at short times, and are not qualitatively or quantitatively important. This is illustrated by comparing the two versions of the theory for representative model systems.