The combination of molecular dynamics simulations and neutron scattering measurements on three different glass-forming polymers (polyisoprene, poly(vinyl ethylene) and polybutadiene) has allowed to establish the existence of a crossover from Gaussian to non-Gaussian behavior for the incoherent scattering function in the α-relaxation regime. The deviation from Gaussian behavior observed can be reproduced assuming the existence of a distribution of discrete jump lengths underlying the sublinear diffusion of the atomic motions during the structural relaxation.

By means of neutron spin echo (NSE) we have explored the dynamics of poly(vinyl ethylene) on length scales covering Rouse dynamics and below. The results establish the simultaneous existence of a generic sublinear diffusion regime which underlies the α-process in addition to the Rouse process. Both regimes are separated by a well-defined dynamic crossover. From that the size of the Gaussian blobs making up the Rouse model is determined directly. The glassy dynamics may thus be identified with subdiffusive motions occurring within these Gaussian blobs.

Non-exponential relaxation is a universal feature of systems as diverse as glasses, spin glasses, earthquakes, financial markets and the universe. Complex relaxation results from hierarchically constrained dynamics with the strength of the constraints being directly related to the form of the relaxation, which changes from a simple exponential to a stretched exponential and a power law by increasing the constraints in the system. A global and unified approach to non-exponentiality was first achieved by Weron and was further generalized by Brouers and Sotolongo-Costa, who applied the concept of non-extensive entropy introduced by Tsallis to the relaxation of disordered systems.

These concepts are now confronted with experimental results on the classical metallic spin glasses CuMn, AuFe and the insulating system EuSrS. The revisited data have also be complemented by new results on several compositions of the classical CuMn spin glass and on systems, like CoGa and CuCo, the magnetic behaviour of which is believed to arise from magnetic clusters and should be characteristic for superparamagnetism.