Vibrational phenomena in glasses at low temperatures captured by field theory of disordered harmonic oscillators

Abstract

We investigate the vibrational properties of topologically disordered materials by analytically studying particles that harmonically oscillate around random positions. Exploiting classical field theory in the thermodynamic limit at $T=0$, we build up a self-consistent model by analyzing the Hessian utilizing Euclidean Random Matrix theory. In accordance with earlier findings [T. S. Grigera et al.J.~Stat.~Mech.~11 (2011) P02015.], we take non-planar diagrams into account to correctly address multiple local scattering events. By doing so, we end up with a first principles theory that can predict the main anomalies of athermal disordered materials, including the boson peak, sound softening, and Rayleigh damping of sound. In the vibrational density of states, the sound modes lead to Debye's law for small frequencies. Additionally, an excess appears in the density of states starting as ${\omega }^4$ in the low frequency limit, which is attributed to (quasi-) localized modes.

final version; 6 pages, 3 figures; 8 pages of supplemental information with 1 figure

References in corpus (5)

• Low-energy quasilocalized excitations in structural glasses
• Low-frequency vibrational spectrum of mean-field disordered systems
• Unifying description of the vibrational anomalies of amorphous materials
• Microscopic analysis of sound attenuation in low-temperature amorphous solids reveals quantitative importance of non-affine effects
• Long-Wavelength Anomalies in the Asymptotic Behavior of Mode-Coupling Theory

Cited by in corpus (10)

• The Origin of Sound Damping in Amorphous Solids: Defects and Beyond
• Properties of stable ensembles of Euclidean random matrices
• On elastic constants of zero-temperature amorphous solids
• A self-consistent current response theory of jamming and vibrational modes in low-temperature amorphous solids
• Effective medium theory for viscoelasticity of soft jammed solids
• Sound Attenuation in Glasses
• Unified study of viscoelasticity and sound damping in hard and soft amorphous solids
• Impact of elastic inhomogeneity on collective dynamical properties investigated by field theoretical description in real space
• The anomalous density of states and quasi-localized vibration through homogeneous thermalization of an inhomogeneous elastic system
• Critical fluctuations of elastic moduli in jammed solids