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Spectral responses in granular compaction

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 $\tildeχ_v$. While the packing density $ρ$ displays glass-like slow relaxations (aging) and history-dependence (memory) at low tapping amplitudes, the susceptibility $\tildeχ_v$ displays very weak aging effects, and its spectrum shows no sign of a rapidly growing timescale. These features place $\tildeχ_v$ in sharp contrast to its dielectric and magnetic counterparts in structural and spin glasses; instead, $\tildeχ_v$ 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.