Universality Classes of Dynamical Behavior

Abstract

In most studies of dynamic correlation functions the focus is on their long-time asymptotic behavior and on the singularity structure of the associated spectral densities. These properties reveal important information on the nature of the physical processes which govern the dynamics of the system under given circumstances. However, the analysis of the same dynamic correlation functions from a quite different perspective can be equally useful and revealing. The focus there is on the properties of spectral densities at high frequencies, specifically their decay law, expressible as in (5.23), in terms of a characteristic exponent λ. The information contained in λ about the underlying dynamical processes is in some sense complementary to that inferred from the singularity structure of spectral densities.