Time correlation functions in Vibration-Transit theory of liquid dynamics

Within the framework of V-T theory of monatomic liquid dynamics, an exact equation is derived for a general equilibrium time correlation function. The purely vibrational contribution to such a function expresses the system's motion in one extended harmonic random valley. This contribution is analytically tractable and has no adjustable parameters. While this contribution alone dominates the thermodynamic properties, both vibrations and transits will make important contributions to time correlation functions. By way of example, the V-T formulation of time correlation functions is applied to the dynamic structure factor S(q,w). The vibrational contribution alone is shown to be in near perfect agreement with low-temperature molecular dynamics simulations, and a model simulating the transit contribution with three adjustable parameters achieves equally good agreement with molecular dynamics results in the liquid regime. The theory indicates that transits will broaden without shifting the Rayleigh and Brillouin peaks in S(q,w), and this behavior is confirmed by the MD calculations. We find the vibrational contribution alone gives the location and much of the width of the liquid-state Brillouin peak. We also discuss this approach to liquid dynamics compared with potential energy landscape formalisms and mode coupling theory, drawing attention to the distinctive features of our approach and to some potential energy landscape results which support our picture of the liquid state.