Universality of anomalous excitations in amorphous solids

A general proof for the universal existence of anomalous, non-Debye harmonic excitations in disordered solids is proposed. Starting from an ideal amorphous solid with fixed mean positions of all atoms and harmonic interactions, it was demonstrated that any increase of disorder leads stringently to an increase of the spectral density for low (and also very high) frequencies. That means, the density of states shows additional contributions to the low-frequency part of the standard Debye density, even though the wavelength of corresponding phonon like excitations is of an order of magnitude on which the amorphous solid is still homogeneous and the sound waves are not strongly effected by the disorder.