Anharmonicity and quasi-localization of the excess low-frequency vibrations in jammed solids

TL;DR

This paper investigates the vibrational properties of jammed solids, revealing a crossover frequency associated with quasi-localized modes and highlighting the unique anharmonic behavior at low frequencies.

Contribution

It provides a detailed comparison of harmonic and anharmonic vibrational modes in jammed packings, identifying a crossover frequency and characterizing the quasi-localization and anharmonicity of low-frequency modes.

Findings

Crossover frequency shifts to zero at the jamming threshold.

Low-frequency modes are quasi-localized and highly anharmonic.

These modes are most responsive to pressure and have low energy barriers.

Abstract

We compare the harmonic and anharmonic properties of the vibrational modes in 3-dimensional jammed packings of frictionless spheres interacting via repulsive, finite range potentials. A crossover frequency is apparent in the density of states, the diffusivity and the participation ratio of the modes. At this frequency, which shifts to zero at the jamming threshold, the vibrational modes have a very small participation ratio implying that the modes are quasi-localized. The most anharmonic modes occur at low frequency which is opposite to what is normally found in crystals. The lowest frequency modes have the strongest response to the pressure and the lowest energy barriers to mechanical failure.