UNIVERSALITY CLASSES FOR ASYMPTOTIC-BEHAVIOR OF RELAXATION PROCESSES IN SYSTEMS WITH DYNAMICAL DISORDER - DYNAMICAL GENERALIZATIONS OF STRETCHED EXPONENTIAL

The asymptotic behavior of multichannel parallel relaxation processes for systems with dynamical disorder is investigated in the limit of a very large number of channels. An individual channel is characterized by a state vector x which, due to dynamical disorder, is a random func tion of time. A limit of the thermodynamic type in the x-space is intr oduced for which both the volume available and the average number of c hannels tend to infinity, but the average volume density of channels r emains constant. Scaling arguments combined with a stochastic renormal ization group approach lead to the identification of two different typ es of universal behavior of the relaxation function corresponding to n onintermittent and intermittent fluctuations, respectively. For nonint ermittent fluctuations a dynamical generalization of the static Huber' s relaxation equation is derived which depends only on the average fun ctional density of channels, p[W(t')]D[W(t')], the channels being clas sified according to their different relaxation rates W = W(t'), which are random functions of time. For intermittent fluctuations a more com plicated relaxation equation is derived which, in addition to the aver age density of channels, p[W(t')]D[W(t')], depends also on a positive fractal exponent H which characterizes the fluctuations of the density of channels. The general theory is applied for constructing dynamical analogs of the stretched exponential relaxation function. For noninte rmittent fluctuations the type of relaxation is determined by the regr ession dynamics of the fluctuations of the relaxation rate. If the reg ression process is fast and described by an exponential attenuation fu nction, then after an initial stretched exponential behavior the relax ation process slows down and it is not fully completed even in the lim it of very large times. For self-similar regression obeying a negative power law, the relaxation process is less sensitive to the influence of dynamical disorder. Both for small and large times the relaxation p rocess is described by stretched exponentials with the same fractal ex ponent as for systems with static disorder. For large times the effici ency of the relaxation process is also slowed down by fluctuations. Si milar patterns are found for intermittent fluctuations with the differ ence that for very large times and a slow regression process a crossov er from a stretched exponential to a self-similar algebraic relaxation function occurs. Some implications of the results for the study of re laxation processes in condensed matter physics and im molecular biolog y are investigated. (C) 1996 American Institute of Physics.