Authors: Paul Spyridis Gene F Mazenko
Publish Date: 2014/01/11
Volume: 154, Issue: 4, Pages: 1030-1056
Abstract
It is well known that mode coupling theory MCT leads to a twostep powerlaw 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 816061102 2010 We show how the powerlaw exponents can be computed in the secondorder approximation where we treat hardsphere fluids with statics described by the Percus–Yevick solutionThis plot shows ftext MCTk sigma = 10 the nonergodicity parameter at wavenumber k sigma = 10 as a function of the packing fraction The dashed line shows a visual fit of Asqrtepsilon + B to the data This confirms our calculation of g in Sect 62In this section we will analyze the asymptotic longtime behavior of phi q t First we need to find out what happens at the critical density so we can match the other solutions to it in the limit epsilon rightarrow 0 The analysis of phi q t at the critical density is essentially the same as in Sect 61 but we include it here for completeness In the nonergodic glass case we have only one long time to consider In the ergodic liquid case there are two time regimes the power law decay as in the solid case followed by the von Schweidler decay To analyze these regimes we rescale the time t by introducing a large constant omega c such that tau = omega c t In this rescaling the power law decay corresponds to tau ll 1 and the von Schweidler decay to tau gg 1
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