Low-frequency vibrations of jammed packings in large spatial dimensions

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Materials science

Background:

• Amorphous packings near jamming are crucial for understanding the vibrational properties of glasses.
• Mean-field theories predict a specific power-law scaling (g(ω)∼ω²) for the vibrational density of states at low frequencies, known as non-Debye scaling.
• Previous numerical studies indicated that finite-dimensional effects cause this scaling to break down at very low frequencies.

Purpose of the Study:

• To investigate the validity range of non-Debye scaling in amorphous packings across various spatial dimensions.
• To determine how dimensionality influences the low-frequency vibrational spectrum of glasses.
• To explore the role of prestress as a parameter for comparing packings in different dimensions.

Main Methods:

• Preparation of amorphous packings with up to 128,000 particles.
• Simulations conducted in spatial dimensions ranging from d=3 to d=9.
• Analysis of the vibrational density of states (g(ω)) to identify scaling behaviors.
• Utilizing prestress as a control parameter for inter-dimensional comparisons.

Main Results:

• Numerical results indicate that non-Debye scaling is observed down to a frequency that decreases with increasing dimensionality (d).
• The breakdown frequency of non-Debye scaling appears to diminish as spatial dimensions increase.
• Prestress is confirmed as an effective parameter for quantitatively comparing amorphous packings across different dimensions.

Conclusions:

• The non-Debye scaling in the vibrational density of states of amorphous packings is consistent with mean-field predictions, especially in higher dimensions.
• Finite-dimensional effects influence the low-frequency vibrational spectrum, causing a shift in the scaling breakdown.
• Prestress provides a robust method for standardizing comparisons of packing properties across varying spatial dimensions.