Power-law Decay and the Ergodic–Nonergodic Transition in Simple Fluids

Abstract

It is well known that mode coupling theory (MCT) leads to a two-step power-law time decay in dense simple fluids. We show that much of the mathematical machinery used in the MCT analysis can be taken over to the analysis of the systematic theory developed in the Fundamental Theory of Statistical Particle Dynamics (Mazenko in Phys Rev E 81(6):061102, 2010). We show how the power-law exponents can be computed in the second-order approximation where we treat hard-sphere fluids with statics described by the Percus–Yevick solution.