Vibrations and Diverging Length Scales Near the Unjamming Transition

2005/01/26 by Leonardo E. Silbert, L. E. Silbert, Andrea J. Liu +3 · 14 citations
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Crossover #Geometry #Limit (mathematics) #Material Dynamics and Properties #Mathematical analysis #Mathematics #Normal mode #Omega #Physics #Power law #Quantum mechanics #Quantum, superfluid, helium dynamics #Scaling #Scaling law #Spectroscopy and Quantum Chemical Studies #Statistics #Vibration #Zero (linguistics) #cond-mat.soft

paper · pdf · doi:10.1103/physrevlett.95.098301

Submitted to PRL, 4 pages + 7 .eps figures

arxiv created 2005/01/26 · openalex publication_date 2005/08/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We numerically study the vibrations of jammed packings of particles interacting with finite-range, repulsive potentials at zero temperature. As the packing fraction \ensuremathφ is lowered towards the onset of unjamming at \ensuremathφ_c, the density of vibrational states approaches a nonzero value in the limit of zero frequency. For \ensuremathφ>\ensuremathφ_c, there is a crossover frequency, \ensuremathω^* below which the density of states drops towards zero. This crossover frequency obeys power-law scaling with \ensuremathφ\mathrm\text\ensuremath-\ensuremathφ_c. Characteristic length scales, determined from the dominant wave vector contributing to the eigenmode at \ensuremathω^*, diverge as power laws at the unjamming transition.

Citations

• Continuum limit of amorphous elastic bodies: A finite-size study of low-frequency harmonic vibrations
• Vibrations in glasses and Euclidean random matrix theory
• Jamming at zero temperature and zero applied stress: The epitome of disorder
• Spatially Heterogeneous Dynamics in Supercooled Liquids

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• Continuum limit of the vibrational properties of amorphous solids
• Rotational sound in disordered granular materials
• Higher-order corrections to the effective potential close to the jamming transition in the perceptron model
• Unjamming Dynamics: The Micromechanics of a Seismic Fault Model
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• Level statistics and Anderson delocalization in two-dimensional granular materials