  The Brillouin peak appears in the dynamic structure factor S(q,w), and the
dispersion curve is the Brillouin peak frequency as function of q. The
theoretical function underlying S(q,w) is the density autocorrelation function
F(q,t). A broadly successful description of time correlation functions is
provided by mode coupling theory, which expresses F(q,t) in terms of processes
through which the density fluctuations decay. In contrast, vibration-transit
(V-T) theory is a Hamiltonian formulation of monatomic liquid dynamics in which
the motion consists of vibrations within a many-particle random valley,
interspersed with nearly instantaneous transits between such valleys. Here, V-T
theory is applied to S(q,w). The theoretical vibrational contribution to S(q,w)
is the sum of independent scattering cross sections from the normal vibrational
modes, and contains no explicit reference to decay processes. For a theoretical
model of liquid Na, we show that the vibrational contribution with no
adjustable parameters gives an excellent account of the Brillouin peak
dispersion curve, as compared to MD calculations and to experimental data.
