Feedback interaction between anharmonic and harmonic modes in glasses

Abstract

The vibration spectrum of a metastable glassy state contains mainly two types of excitations: harmonic (phonons) and anharmonic modes (AM), some of which are double-well potentials. The AMs are treated in terms of the catastrophe theory. Two possible representations of the potential of the AMs are discussed. The double-well potentials correspond to only a minor part of the AMs, while the major part corresponds to soft anharmonic vibrations that are experimentally observed as a shift of the density of vibrational states towards lower frequencies. Strong feedback interaction between the anharmonic and harmonic modes results in the appearance of higher-rank AMs, making a hierarchy in which the higher-rank AMs are responsible for stability of the corresponding lower-rank AM. A simple two-level hierarchy simulating the relaxation process of the glassy state is considered. The characteristic activation energy for this process decreases with temperature.