  We study the collective excitation spectrum of a d=3 site-disordered
Anderson-Hubbard model at half-filling, via a random-phase approximation (RPA)
about broken-symmetry, inhomogeneous unrestricted Hartree-Fock (UHF) ground
states. We focus in particular on the density and character of low-frequency
collective excitations in the transverse spin channel. In the absence of
disorder, these are found to be spin-wave-like for all but very weak
interaction strengths, extending down to zero frequency and separated from a
Stoner-like band, to which there is a gap. With disorder present, a prominent
spin-wave-like band is found to persist over a wide region of the
disorder-interaction phase plane in which the mean-field ground state is a
disordered antiferromagnet, despite the closure of the UHF single-particle gap.
Site resolution of the RPA excitations leads to a microscopic rationalization
of the evolution of the spectrum with disorder and interaction strength, and
enables the observed localization properties to be interpreted in terms of the
fraction of strong local moments and their site-differential distribution.
