Dynamical model of the liquid-glass transition

Abstract

Based on a microscopic theory developed recently, a dynamical model of density fluctuations in simple fluids and glasses is proposed and analyzed analytically and numerically. The model exhibits a liquid-glass transition, where the glassy phase is characterized by a zero-frequency pole of the longitudinal and transverse viscosities indicating the systems' stability against stress. This also implies an elastic peak in the density-fluctuation spectrum. Approaching the glass transition the slowing down of density fluctuations is controlled by the increasing longitudinal viscosity, which in turn is coupled via a nonlinear feedback mechanism to the slowly decaying density fluctuations. This causes a divergence of the structural relaxation time at a certain critical coupling constant ${\lambda }_c$. At the glass transition density fluctuations decay with a long-time power law $\Phi \mathrm{}\left(t\right)\mathrm{}\sim t^{-\alpha }$ with $\alpha =0.395\mathrm{}$ and approaching the transition the viscosity diverges proportional to ${\epsilon }^{-\mu }$ and ${\epsilon }^{-\mu }$, where $\epsilon =|1-\frac{\lambda }{{\lambda }_c}|$ and $\mu =\frac{(1+\alpha )}{2\alpha }$, ${\mu }^{\prime }=\mu -1\mathrm{}$ below and above the transition, respectively. The long-time tail "paradox" in dense fluids is briefly discussed.