The anomalous density of states and quasi-localized vibration through homogeneous thermalization of an inhomogeneous elastic system

Abstract

Amorphous solids are dynamically inhomogeneous due to in lack of translational symmetry and hence exhibit vibrational properties different from crystalline solids with anomalous low frequency vibrational density of states (VDOS) and related low temperature thermal properties. However, an interpretation of their origin from basic physical laws is still needed compared with rapidly progressed particle level investigations. In this work, we start with the quasi-equilibrium condition, which requires elastic potential energy to be homogeneously distributed even in an inhomogeneous elastic solid over long time observation. Analytical result shows that the anomalous low frequency VDOS behavior $D(\omega )\propto {\omega }^4$ can be obtained when the quasi-equilibrium condition is satisfied on an inhomogeneous elastic system. Under high frequency after a crossover depending on the length scale of inhomogeneity, the power law of VDOS is changed to square $D(\omega )\propto {\omega }^2$ which is Debye's law for crystalline solids. These features agree with recent particle level investigations. Our work suggest that the universal low frequency anomaly of amorphous solids can be considered as a result of homogeneous thermalization.

References in corpus (8)

• DYNASOR -- A tool for extracting dynamical structure factors and current correlation functions from molecular dynamics simulations
• Theory of sound attenuation in amorphous solids from nonaffine motions
• Stringlet Excitation Model of the Boson Peak
• Vibrational phenomena in glasses at low temperatures captured by field theory of disordered harmonic oscillators
• Phonons in stringlet-land and the boson peak
• Quasi-localized vibrational modes, Boson peak and sound attenuation in model mass-spring networks
• Dispersionless Flat Mode and Vibrational Anomaly in Active Brownian Vibrators Induced by String-like Dynamical Defects
• Unified study of viscoelasticity and sound damping in hard and soft amorphous solids

Cited by in corpus (1)

• Impact of elastic inhomogeneity on collective dynamical properties investigated by field theoretical description in real space