Dynamical model of the liquid-glass transition

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 λ_c. At the glass transition density fluctuations decay with a long-time power law Φ(t)∼t^-α with α=0.395 and approaching the transition the viscosity diverges proportional to ε^-μ and ε^-μ, where ε=|1-λ/λ_c| and μ=(1+α)/2α, μ^′=μ-1 below and above the transition, respectively. The long-time tail "paradox" in dense fluids is briefly discussed.