Numerical Study of Roton-Like Collective Excitations in Glassy Materials

Roton-like collective excitations of non-quantum origin have been recognized for quite a long time in many structurally disordered materials. A classical study is attempted of a computer-quenched Lennard-Jones glass in the present article. We show that the collective excitations involve vortex motions, as argued by Feynman for quantum liquids. Adopting the harmonic approximation, we constructed the dynamical structure factor and calculated its eigenvectors at several frequencies in order to visualize the respective atomic motions. Some of them are just like those predicted by Feynman, although we obtained them irrelevant of the Bose statistics. We also calculated the dynamical structure factor and confirmed the characteristic roton minimum in the dispersion relation, which is quantitatively close to that observed for liquid Ar.