Vibrational density of states and specific heat in glasses from random matrix theory

Abstract

The low-temperature properties of glasses present important differences with respect to crystalline matter. In particular, models such as the Debye model of solids, which assume the existence of an underlying regular lattice, predict that the specific heat of solids varies with the cube of temperature at low temperatures. Since the 1970s' at least, it is a well established experimental fact that the specific heat of glasses is instead just linear in $T$ at $T\sim 1K$, and presents a pronounced peak when normalized by $T^3$, known as the boson peak. Here we present a new approach which suggests that the vibrational and thermal properties of amorphous solids are affected by the random matrix part of the vibrational spectrum. The model is also able to reproduce, for the first time, the experimentally observed inverse proportionality between the boson peak in the specific heat and the shear modulus.

arXiv commentv5: title corrected to match the published version in PRE

References in corpus (27)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Vibrations and diverging length scales near the unjamming transition
• Approximate analytical description of the nonaffine response of amorphous solids
• Universal Spectrum of Normal Modes in Low-Temperature Glasses: an Exact Solution
• The Origin of the Boson Peak and the Thermal Conductivity Plateau in Low Temperature Glasses
• Anharmonicity and quasi-localization of the excess low-frequency vibrations in jammed solids
• Local inversion-symmetry breaking controls the boson peak in glasses and crystals
• Sparse random matrices: the eigenvalue spectrum revisited
• Suppression of tunneling two-level systems in ultrastable glasses of indomethacin
• The Ioffe-Regel criterion and diffusion of vibrations in random lattices
• The simplest model of jamming
• Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems
• The Intrinsic Quantum Excitations of Low Temperature Glasses
• The "Tunneling Two-Level Systems" Model of the Low-Temperature Properties of Glasses: Are "Smoking-Gun" Tests Possible?
• Vibrations in glasses and Euclidean Random Matrix theory
• Mean-field model for the density of states of jammed soft spheres
• A random matrix definition of the boson peak
• A simple random matrix model for the vibrational spectrum of jammed packings
• Hydrodynamics of disordered marginally-stable matter
• Local Properties of the Potential Energy Landscape of a Model Glass: Understanding the Low Temperature Anomalies
• A unifying model for random matrix theory in arbitrary space dimensions
• Strain dependence of the acoustic properties of amorphous metals below 1K: Evidence for the interaction between tunneling states
• Density of states in random lattices with translational invariance
• Impact of jamming criticality on low-temperature anomalies in structural glasses
• Soft modes in jammed hard spheres (I): Mean field theory of the isostatic transition
• Proof of a conjecture on the infinite dimension limit of a unifying model for random matrix theory
• Rigidity-based approach to the boson peak in amorphous solids: from sphere packing to amorphous silica

Cited by in corpus (15)

• Depletion of two-level systems in ultrastable computer-generated glasses
• Relaxation and vibrational properties in metal alloys and other disordered systems
• Unified theory of vibrational spectra in amorphous materials
• A random matrix approach to the boson peak and Ioffe-Regel criterion in amorphous solids
• Field Theory of Dissipative Systems with Gapped Momentum States
• Universal non-Debye low-frequency vibrations in sheared amorphous solids
• Complete mathematical theory of the jamming transition: A perspective
• Emergence of two-level systems in glass formers: a kinetic Monte Carlo study
• A new paradigm for the low-T glassy-like thermal properties of solids
• Drive-specific adaptation in disordered mechanical networks of bistable springs
• Physics of Phonon-Polaritons in Amorphous Materials
• Level statistics and Anderson delocalization in two-dimensional granular materials
• Vibrational density of states of jammed packing: mean-field theory
• Dynamics of Disordered Mechanical Systems with Large Connectivity, Free Probability Theory, and Quasi-Hermitian Random Matrices
• Singularities in Hessian element distributions of amorphous media