Interaction of quasilocal harmonic modes and boson peak in glasses

The properties of harmonic vibrational excitations indisordered media and glasses become now a very activetopic of scientific research [1]. Contrary to the quite wellestablished behavior of electrons in disordered conduc-tors there is no consensus at all regarding the harmonicvibrations in ordinary glasses. The most common andchallenging of their signatures is the so-called boson peakobserved in numerous experiments in the low-frequencyRaman and inelastic neutron scattering. The physicalorigin of the peak is however still a matter of great de-bates. The common view is that the solution of this prob-lem is a corner-stone for our veritable understanding ofglassy vibrational dynamics.The main discussion in the literature involves now thequestion whether the harmonic vibrations responsible forthe boson peak are propagating plane waves (phononlike) [2] or localized because of disorder [3]. The thirdpossibility, which we share in this paper, is that theyare neither propagating waves nor localized but have adiffusive nature [4].For the solution of this crucial question quite power-ful and expensive experimental techniques are now in use.First ofall these are Raman experiments themselves. Butsince visible light due to energy and momentum conser-vation laws does not interact properly with sound-like ex-citations, one has to use two other possibilities, namelyinelastic X-ray and neutron scattering.The main difficulty in the inelastic X-ray scattering ex-periments is the very high incident photon energy (≃ 20KeV), and its relatively small change, of the order of10