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

Bongsoo Kim; Kyozi Kawasaki; Hugo Jacquin; Frédéric van Wijland

doi:10.1103/physreve.89.012150

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arXiv · 1307.1359

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

Bongsoo Kim·Kyozi Kawasaki·Hugo Jacquin·Frédéric van Wijland

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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.

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Bongsoo Kim, Kyozi Kawasaki, Hugo Jacquin, Frédéric van Wijland. 2013-07-04. Equilibrium dynamics of the Dean-Kawasaki model: MCT and beyond. https://doi.org/10.1103/physreve.89.012150

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