THEORETICAL ASPECTS OF COUPLING MODEL SCHEMES OF SLOW RELAXATION IN COMPLEX CORRELATED SYSTEMS

Experimental data of temporal relaxation phenomena in diverse types of complex correlated condensed matter systems seem to follow stretched exponential behavior (or its frequency space counterpart). Descriptions of such phenomena based on 'coupling model' schemes invoke three timescales: tau-0 associated with an early linear exponential; tau* associated with a late stretched exponential with a stretching index n (0 less-than-or-equal-to n < 1); and omega-c-1, the time of onset of the effect of coupling (correlation) which enters into a relation between tau-0 and tau*, namely, omega-c-tau* = [(1 - n)-omega-c-tau-0]1/1 - n. Tau-0 represents the relaxation time before correlations become operative and tau* is the relaxation time when correlations are operative. 'Coupling model' schemes described here have been successful in bringing together a large body of experimental data for a significant class of complex correlated systems (CCS) and demonstrate certain widely shared behaviors. A review of the conceptual notions used in coupling model schemes in the past decade is outlined. The scope and underlying assumptions of these schemes are made explicit. In an appendix, a general phenomenology that brings out the dynamic structure of relaxation in CCS is also outlined.