Elements of Liquid Dynamics
In this chapter, the general concepts are introduced, which are used to describe simple-liquid dynamics. The hydrodynamic-limit expressions are derived for the correlation functions, which are formed with the small-wave-number fluctuations of the conserved densities. Langevin's theory for the velocity correlations, Maxwell's model for visco-elastic effects, and Mountain's formulas for the central peak of the density-fluctuation spectra are deduced from the assumption of a separation of the time scale for the correlation decay of currents and stresses from that specifying the reduced dynamics of the decay-causing fluctuating forces. The chapter explains that the onset of glassy dynamics is related to an increasing violation of the time-scale-separation property. Ideal glass states manifest themselves by the simultaneous occurrence of arrested parts of the correlations for density fluctuations and for fluctuating forces.
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