  The first goal of Vibration-Transit (V-T) theory was to construct a tractable
approximate Hamiltonian from which the equilibrium thermodynamic properties of
monatomic liquids can be calculated. The Hamiltonian for vibrations in an
infinitely extended harmonic random valley, together with the universal
multiplicity of such valleys, gives an accurate first-principles account of the
measured thermodynamic properties of the elemental liquids at melt. In the
present paper, V-T theory is extended to non-equilibrium properties, through an
application to the dynamic structure factor S(q,w). It was previously shown
that the vibrational contribution alone accurately accounts for the Brillouin
peak dispersion curve for liquid sodium, as compared both with MD calculations
and inelastic x-ray scattering data. Here it is argued that the major effects
of transits will be to disrupt correlations within the normal mode vibrational
motion, and to provide an additional source of inelastic scattering. We
construct a parameterized model for these effects, and show that it is capable
of fitting MD results for S(q,w) in liquid sodium. A small discrepancy between
model and MD at large q is attributed to multimode vibrational scattering. In
comparison, mode coupling theory formulates S(q,w) in terms of processes
through which density fluctuations decay. While mode coupling theory is also
capable of modeling S(q,w) very well, V-T theory is the more universal since it
expresses all statistical averages, thermodynamic functions and time
correlation functions alike, in terms of the same motional constituents,
vibrations and transits.
