  A model for weakly excited granular media is derived by combining the free
volume argument of Nowak et al. [Phys. Rev. E 57, 1971 (1998)] and the
phenomenological model for supercooled liquids of Adam and Gibbs [J. Chem.
Phys. 43, 139 (1965)]. This is made possible by relating the granular
excitation parameter \Gamma, defined as the peak acceleration of the driving
pulse scaled by gravity, to a temperature-like parameter \eta(\Gamma). The
resulting master equation is formally identical to that of Bouchaud's trap
model for glasses [J. Phys. I 2, 1705 (1992)]. Analytic and simulation results
are shown to compare favourably with a range of known experimental behaviour.
This includes the logarithmic densification and power spectrum of fluctuations
under constant \eta, the annealing curve when \eta is varied cyclically in
time, and memory effects observed for a discontinuous shift in \eta. Finally,
we discuss the physical interpretation of the model parameters and suggest
further experiments for this class of systems.
