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The existence of a constant density of two-level systems (TLS) was proposedas the basis of some intriguing universal aspects of glasses at ultra-lowtemperatures. Here we ask whether their existence is necessary for explainingthe universal density of states quasi-localized modes (QLM) in glasses atultra-low temperatures. A careful examination of the QLM that exist in ageneric atomistic model of a glass former reveals at least two types of them,each exhibiting a different density of states, one depending on the frequencyas $\omega^3$ and the other as $\omega^4$. The properties of the glassy energylandscape that is responsible for the two types of modes is examined here,explaining the analytic feature responsible for the creations of (at least) twofamilies of QLM's. Although adjacent wells certainly exist in the complexenergy landscape of glasses, doubt is cast on the relevance of TLS for theuniversal density of QLM's.

Density of Quasi-localized Modes in Glasses: where are the Two-Level Systems?