Nonequilibrium mode-coupling theory for uniformly sheared systems

TL;DR

This paper develops a nonequilibrium mode-coupling theory for uniformly sheared systems, connecting microscopic dynamics to stationary rheological properties using projection-operator formalism and transient density correlators.

Contribution

It introduces a novel theoretical framework based on microscopic equations of motion to describe steady-state properties of sheared systems, extending mode-coupling theory.

Findings

Formulates self-consistent equations for transient density correlators.

Expresses stationary properties in terms of transient correlators.

Provides detailed comparison with existing Smoluchowski-based mode-coupling theory.

Abstract

We develop a nonequilibrium mode-coupling theory for uniformly sheared systems starting from microscopic, thermostatted SLLOD equations of motion. Our theory aims at describing stationary-state properties including rheological ones of sheared systems, and this is accomplished via two steps. Firstly, a set of self-consistent equations is formulated based on the projection-operator formalism and on the mode-coupling approach for the transient density correlators which measure the correlations between the density fluctuations in the initial equilibrium state and the ones at later times after the shearing force is turned on. The transient time-correlation function formalism is then used which, combined with the mode-coupling approximation, expresses stationary-state properties in terms of the transient density correlators. A detailed comparison of our theory is also presented with the related mode-coupling theory which is based on the Smoluchowski equation for Brownian particles under stationary shearing.