A theory for the beta -relaxation process near the liquid-to-glass crossover

The mode coupling theory for supercooled liquid dynamics finds a beta -relaxation regime on mesoscopic timescales. It is caused by the interplay between nonlinear interactions of density fluctuations and phonon-assisted hopping transport. In this regime all correlation functions and spectra can be expressed in terms of a single beta -correlator G, which is a homogeneous function of time and two relevant control parameters. For temperatures T sufficiently above the critical value T_c hopping effects can be neglected and a stretched susceptibility minimum, is found as a crossover from von Schweidler decay to critical decay. For T near T_c hopping effects balance the cage effect and this results on logarithmic scales in a rather abrupt crossover from the high-frequency alpha -peak tail to the critical spectrum. For T below T_c there appears a frequency window between two knees in the susceptibility spectrum, where hopping effects suppress the enhanced fractal spectra. There occurs a crossover from Debye relaxation to white noise. The resulting susceptibility minimum in the strongly supercooled state exhibits a subtle power law dependence on the separation parameter T-T_c.