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The effect of a non-linear oscillator's vibrations (either in solids or in liquids) is the primary source of the amorphous state of the matter. The number of nonlinear oscillators (N.Os.) is considered to be very small at Tg (approximately 2.5%), and rises with the increase in temperature, reaching approximately 100% at the critical temperature Tc. In the main transition zone (covering the area between Tg and the crossover temperature Tcr), there are high amplitudes of N.Os. restricted by the particle neighbors and also by the internal energy related to the shear modulus. The shear modulus disappears above the Tcr, where the matter exists either in the form of a liquid or in the form of a rubber-like state (which is not considered in this study). In the present study, the liquid is considered as a heterogeneous structure, formed on the one hand by domains, which are responsible for the linear viscoelastic behavior, and on the other hand with the stand alone N.Os., which act as the trembling motion sources of the optically observed aspect of Brownian motion. Under the Tcr and Tg temperatures, the secondary β and tertiary γ processes are studied as well

The Glassy State as the Lawfully Disarranged State. Vibration Uncertainty and Chaos-Like Movements