Character of Atomic Vibrations in a Lennard-Jones Glass

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Lennard-Jones glasses (made on a computer by quenching from liquid state coordinates) are studied in harmonic approximation. Vibrational eigenfrequencies and eigenvectors are found by exact diagonalization for models with periodic boundaries and N=(500, 2048, and 6980) atoms. We analyze the density of states, mobility edge, and bond-stretching character of the normal modes. In agreement with older work of Grest, Nagel, and Rahman, the upper 7% of modes are localized, and the rest, delocalized. We find that modes can not be differentiated by any property or quantum number except their eigenfrequency. More specifically, in a given narrow frequency interval, all modes are globally identical. Transverse or longitudinal character, for example, disappears.