Excitations of Atomic Vibrations in Amorphous Solids

We study excitations of atomic vibrations in the reciprocal space for amorphous solids. There are two kinds of excitations we obtained, collective excitation and local excitation. The collective excitation is the collective vibration of atoms in the amorphous solids while the local excitation is stimulated locally by a single atom vibrating in the solids. We introduce a continuous wave vector for the study and transform the equations of atomic vibrations from the real space to the reciprocal space. We take the amorphous silicon as an example and calculate the structures of the excitations in the reciprocal space. Results show that an excitation is a wave packet composed of a collection of plane waves. We also find a periodical structure in the reciprocal space for the collective excitation with longitudinal vibrations, which is originated from the local order of the structure in the real space of the amorphous solid.