Spectral responses in granular compaction

TL;DR

This paper investigates the spectral response of granular compaction, revealing slow relaxations and weak aging effects that differ from traditional glassy systems, and explores how system size influences these dynamics.

Contribution

It introduces the complex volumetric susceptibility as a new probe for granular dynamics and compares its behavior to glassy systems, highlighting the role of rare relaxation processes.

Findings

$ ilde{ ho}$ shows glass-like aging and memory effects.

$ ilde{oldsymbol{ ext{χ}}}_v$ exhibits weak aging and no rapidly growing timescale.

Finite size effects suppress large-scale particle rearrangements.

Abstract

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.