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The vibrational spectra of solids, both ordered and amorphous, in thelow-energy regime, control the thermal and transport properties of materials,from heat capacity to heat conduction, electron-phonon couplings, conventionalsuperconductivity etc. The old Debye model of vibrational spectra at low energygives the vibrational density of states (VDOS) as proportional to the frequencysquared, but in many materials the spectrum departs from this law which resultsin a peak upon normalizing the VDOS by frequency squared, which is known as the"boson peak". A description of the VDOS of solids (both crystals and glasses)is presented starting from first principles. Without using any assumptionswhatsoever about the existence and nature of "disorder" in the material, it isshown that the boson peak in the VDOS of both ordered crystals and glassesarises naturally from the competition between elastic mode propagation andviscous damping. The theory explains the recent experimental observations ofboson peak in perfectly ordered crystals, which cannot be explained based onprevious theoretical frameworks. The theory also explains, for the first time,how the vibrational spectrum changes with the atomic density of the solid, andexplains recent experimental observations of this effect.

Universal origin of boson peak vibrational anomalies in ordered crystals and in amorphous materials