From disordered crystal to glass — exact theory

Universality in the Vibrational Spectra of Single-Component Amorphous Clusters

“…We check our results regarding the evolution of the vibrational spectrum with the predictions of some existing theoretical works in which disorder itself is modelled in a specific fashion [85][86][87][88][89][90]. In contrast, we model only the interaction between the particles.…”

“…At the same time there is a continuous change in the nature of the associated vibrational spectrum. the data available in this figure with the results presented by Mattis and coworkers for some model calculations on the evolution of the density states as the strength of disorder changes [85][86][87][88][89][90]. These calculations are for a quantum mechanical model of vibration in which a specific model term is included in the Hamiltonian to describe the effect of disorder.…”

“…cubic lattice, they are the following[90]:(1) For any finite value of the disorder parameter there are no van-Hove singularities. (2) As the strength of the disorder parameter increases, more and more modes are transferred to the domains with the lowest and highest frequencies.…”

Dynamical aspects of disorder in condensed matter

“…Also, an estimate of the thermal conductivity, which is obviously controlled by the phonon mean-free-path, shows a crossover from a low-frequency, weak-phonon-scattering regime to a high-frequency, strong-scattering domain for frequencies comparable to or higher than those corresponding to the boson peak maximum. A similar endeavour accounting for anharmonic interactions (Yañez et al 2001) yields qualitatively similar features but also provides estimates for some significant thermodynamic functions. In this latter case, the lattice dynamics are studied in terms of a dynamical Hamiltonian that includes the quadratic (harmonic oscillator) term, a scattering term given in terms of random scattering amplitudes, a parameter that controls the strength of the disorder and a quartic (anharmonic) term whose strength is controlled by a generalized Grüneisen parameter.…”