The problem of glass formation and the low frequency vibrational modes anomalies

Abstract

In this article, we give a short review of the theoretical problems concerning the formation of disordered materials (known as glasses). Then we show how this problem is related to the anomalies in the low frequency vibrational modes observed in glasses. Rigidity theory and the energy landscape topology picture is used to decode how this relationship is built for network glasses. Finally, the problem of the speed of cooling and the ability to reach thermal equilibrium in glasses is explored using a simple model with non-linear interactions. The results are also interesting in soft-matter and protein folding.