Density of quasi-localized modes in athermal glasses

A careful examination of the Quasi-Localized Modes (QLMs) that exist in a generic atomistic model of a glass former reveals at least two types of them, each exhibiting a different density of states, one depending on the frequency as $\omega^3$ and the other as $\omega^4$ . The properties of the glassy energy landscape that is responsible for the two types of modes is examined here, explaining the analytic feature responsible for the creations of (at least) two families of QLMs. It is argued that the QLMs that are revealed by diagonalizing the Hessian matrix are not related to possibly existing Two-Level Systems (TLS)