Numerical studies for localization-delocalization transition in vibrational spectra

By investigating the localization-delocalization transition (LDT) in the instantaneous-normal-mode spectrum of a simple fluid, we compare two numerical methods, the level-spacing statistics and the multifractal analysis, for determining the LDT in vibrational spectra. Both methods are based on scale invariance at the transition. Within numerical errors, our results of the two methods give a reasonable agreement on the location of the transition.