Note: Relaxation time below jamming

Abstract

Like other critical phenomena, the jamming transition accompanies the divergence of the relaxation time $\tau$. A recent numerical study of frictionless spherical particles proves that $\tau$ is inversely proportional to the lowest non-zero eigenvalue ${\lambda }_1$ of the dynamical matrix. In this note, we derive the scaling of ${\lambda }_1$ below the jamming transition point ${\phi }_J$ by solving the linearized dynamical equation. The resultant critical exponent agrees with a previous theoretical result for sheared suspension obtained by applying the virtual work theorem to a simple shear, highlighting the universality of the relaxation dynamics below jamming.

2 pages, 1 figure

References in corpus (3)

• Fractal free energy landscapes in structural glasses
• Jamming in finite systems: stability, anisotropy, fluctuations and scaling
• Unified Theory of Inertial Granular Flows and Non-Brownian Suspensions