Amorphous Solid Vibrational Modes

Soft modes, boson peak, and participation ratio in disordered solids

Parameters

Boson peak ω_BP
Soft modes (<0.5)
Participation ratio
Boson peak: excess low-frequency modes in glasses above Debye (ω²) baseline. DOS/ω² shows a peak.
Soft modes: near-zero frequency — quasi-localized, rearrangement precursors.
Participation ratio: PR=1 (delocalized), PR~1/N (localized).