Instantaneous normal modes of Na in supercooled liquid and glassy states

The instantaneous-normal-mode (INM) densities of states (DOS) of Na in the supercooled-liquid and glassy states under constant pressure have been calculated via molecular-dynamics simulation, with a rapid quenching rate for the glassy states. In the glassy states, at frequencies less than (Formula presented) the frequency corresponding to the lowest-lying traveling waves permitted by the simulated system, the real-frequency INM DOS, strongly deviates from the liquidlike behavior, which is linearly dependent in frequency, but still has a great enhancement as compared with the phonon DOS of the Debye model for crystals. At (Formula presented) peaks in the distribution of the INM participation ratio are observed at frequencies around (Formula presented) and (Formula presented) the latter corresponding to the second lowest-lying traveling waves.