Equilibrium dynamics of the Dean-Kawasaki model: MCT and beyond

TL;DR

This paper develops an extended theoretical framework for the equilibrium dynamics of the Dean-Kawasaki model, incorporating additional correlation functions and revealing differences from traditional Mode-Coupling Theory, especially regarding ergodic transitions.

Contribution

It introduces a new set of three coupled equations for density and its logarithm correlations, generalizing Mode-Coupling Theory without assuming ergodic-non ergodic transitions.

Findings

New equations involve density and its logarithm correlations.

The extended model does not predict ergodic-non ergodic transition.

The approach accounts for noninteracting Brownian gas behavior.

Abstract

We extend a previously proposed field-theoretic self-consistent perturbation approach for the equilibrium dynamics of the Dean-Kawasaki equation presented in [J. Stat. Mech. 2008 P02004]. By taking terms missing in the latter analysis into account we arrive at a set of three new equations for correlation functions of the system. These correlations involve the density and its logarithm as local observables. Our new one-loop equations, which must carefully deal with the noninteracting Brownian gas theory, are more general than the historic Mode-Coupling one in that a further and well-defined approximation leads back to the original mode-coupling equation for the density correlations alone. However, without performing any further approximation step, our set of three equations does not feature any ergodic-non ergodic transition, as opposed to the historical mode- coupling approach.