Slow dynamics of linear relaxation systems

Linear relaxation, occurring in dielectrics, viscoelastic fluids, and many other systems, is often characterized by a broad continuous spectrum. We show that the relaxation behavior may be analyzed effectively by means of N-point Padé approximants, applied in the complex plane of the square root of frequency. The method leads to a compact analytic expression for the Laplace transform of the relaxation function, characterized by a small number of poles and their residues in the square root of frequency plane. We study the method in detail for a model of diffusion in three dimensions with a single or double radial potential barrier, and demonstrate its use in the analysis of the viscoelastic relaxation spectrum of polyisobutylene.