Vibrational instability, two-level systems, and the boson peak in glasses

We show that the same physical mechanism is fundamental for two seemingly different phenomena such as the formation of two-level systems in glasses and the boson peak in the reduced density of low-frequency vibrational states g(omega)/omega(2). This mechanism is the vibrational instability of weakly interacting harmonic modes. Below some frequency omega(c) W, the typical value of C and, therefore, the number of active two-level systems is very small, less than 1 per 1x10(7) of oscillators, in good agreement with experiment. Within the unified approach developed in the present paper, the density of the tunneling states and the density of vibrational states at the boson peak frequency are interrelated.