title: Equilibrium dynamics of the Dean-Kawasaki equation: mode-coupling theory and its extension.
abstract: We extend a previously proposed field-theoretic self-consistent perturbation approach for the equilibrium dynamics of the Dean-Kawasaki equation presented in [Kim and Kawasaki, 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 approximation corresponding to Gaussian density fluctuations 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-nonergodic transition, as opposed to the historical mode-coupling approach.
authors.affiliation: Department of Physics and Institute for Soft and Bio Matter Science, Changwon National University, Changwon 641-773, Korea.
authors.forename: Bongsoo
authors.initials: B
authors.lastname: Kim
authors.affiliation: Department of Physics, Faculty of Science, Kyushu University, Fukuoka 812-8581, Japan.
authors.forename: Kyozi
authors.initials: K
authors.lastname: Kawasaki
authors.affiliation: Laboratoire Matière et Systèmes Complexes, UMR7057 CNRS/Paris 7, Université Denis Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France and Laboratoire de Physique, UMR5672 CNRS/ENS Lyon, École Normale Supérieure de Lyon, 46 allé d'Italie, 69364 Lyon Cedex 7, France.
authors.forename: Hugo
authors.initials: H
authors.lastname: Jacquin
authors.affiliation: Laboratoire Matière et Systèmes Complexes, UMR7057 CNRS/Paris 7, Université Denis Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France.
authors.forename: Frédéric
authors.initials: F
authors.lastname: van Wijland