Model of high frequency vibrational dynamics in glasses: strong hybridisation of acoustic and soft mode excitations in Ioffe-Regel crossover

A theoretical model of the vibrational 'high frequency dynamics', including both the boson peak and, above it, the accompanying 'high frequency sound', is proposed for glass. The model is a topologically disordered elastic continuum that contains both soft mode vibrational excitations and standard acoustic vibrations, interacting with each other and becoming strongly hybridised in an Ioffe-Regel crossover. The derived spectrum of the renormalised excitations looks as if the acoustic branch is broken into two parts separated by a narrow pseudo-gap. The reduced vibrational density-of-states is calculated, exhibiting features similar to those of the boson peak and high frequency sound.