Gaussian density fluctuations, mode coupling theory, and all that

TL;DR

This paper compares a solvable toy model for colloidal glassy dynamics with mode coupling theory, revealing differences in predicted particle localization and diffusion behavior under Gaussian static fluctuation assumptions.

Contribution

It introduces an exact solution for a simplified model of glassy dynamics and contrasts it with mode coupling theory predictions, highlighting the impact of static fluctuation assumptions.

Findings

The toy model predicts always diffusive motion under Gaussian assumptions.

Mode coupling theory predicts particle localization at high obstacle densities.

The exact solution differs from MCT, questioning its assumptions in glassy dynamics.

Abstract

We consider a toy model for glassy dynamics of colloidal suspensions: a single Brownian particle diffusing among immobile obstacles. If Gaussian factorization of static density fluctuations is assumed, this model can be solved without factorization approximation for any dynamic correlation function. The solution differs from that obtained from the ideal mode coupling theory (MCT). The latter is equivalent to including only some, positive definite terms in an expression for the memory function. An approximate re-summation of the complete expression suggests that, under the assumption of Gaussian factorization of static fluctuations, mobile particle's motion is always diffusive. In contrast, MCT predicts that the mobile particle becomes localized at a high enough obstacle density. We discuss the implications of these results for models for glassy dynamics.