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Closed nonlinear equations are derived for a self-consistent treatment of density propagation, self-diffusion and current relaxation in a classical monatomic fluid. The solution for a hard-sphere model system brings out a phase transition to a glass at the packing fraction 0.516. Approaching the transition from the glass side the particle mean-square displacement increases to a finite value. A simplified model is analysed in detail. Approaching the transition from the liquid side the diffusivity is predicted to decrease to zero with a power law with exponent 1.76 which the authors find to agree well with some experimental data. The low-frequency density spectrum is found to consist of two contributions; one is an elastic line of the frozen structure on the glass side, which then decays to a narrow diffusion broadened quasielastic peak on the fluid side; the other part is described by a dynamical scaling law and it yields in particular a spectrum diverging at the glass point with certain exponents.
Bengtzelius et al. (Fri,) studied this question.