Localization threshold of Instantaneous Normal Modes from level-spacing   statistics
  We study the statistics of level-spacing of Instantaneous Normal Modes in a supercooled liquid. A detailed analysis allows to determine the mobility edge separating extended and localized modes in the negative tail of the density of states. We find that at temperature below the mode coupling temperature only a very small fraction of negative eigenmodes are localized. 
Stefano Ciliberti, Tomas S. Grigera