  The slow compaction of a gently tapped granular packing is reminiscent of the
low-temperature dynamics of structural and spin glasses. Here, I probe the
dynamical spectrum of granular compaction by measuring a complex
(frequency-dependent) volumetric susceptibility $\tilde{\chi}_v$. While the
packing density $\rho$ displays glass-like slow relaxations (aging) and
history-dependence (memory) at low tapping amplitudes, the susceptibility
$\tilde{\chi}_v$ displays very weak aging effects, and its spectrum shows no
sign of a rapidly growing timescale. These features place $\tilde{\chi}_v$ in
sharp contrast to its dielectric and magnetic counterparts in structural and
spin glasses; instead, $\tilde\chi_v$ bears close similarities to the complex
specific heat of spin glasses. This, I suggest, indicates the glass-like
dynamics in granular compaction are governed by statistically rare relaxation
processes that become increasingly separated in timescale from the typical
relaxations of the system. Finally, I examine the effect of finite system size
on the spectrum of compaction dynamics. Starting from the ansatz that low
frequency processes correspond to large scale particle rearrangements, I
suggest the observed finite size effects are consistent with the suppression of
large-scale collective rearrangements in small systems.
