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Ivanov-Anderson (IA) model (and an earlier treatment by Kubo) envisages adecay of the orientational correlation by random but large amplitude molecularjumps, as opposed to infinitesimal small jumps assumed in Brownian diffusion.Recent computer simulation studies on water and supercooled liquids have shownthat large amplitude motions may indeed be more of a rule than exception.Existing theoretical studies on jump diffusion mostly assume an exponential(Poissonian) waiting time distribution for jumps, thereby again leading to anexponential decay. Here we extend the existing formalism of Ivanov and Andersonto include an algebraic waiting time distribution between two jumps. As aresult, the first and second rank orientational time correlation functions showthe same long time power law, but their short time decay behavior is quitedifferent. The predicted Cole-Cole plot of dielectric relaxation reproducesvarious features of non-Debye behaviour observed experimentally. We alsodeveloped a theory where both unrestricted small jumps and large angular jumpscoexist simultaneously. The small jumps are shown to have a large effect on thelong time decay, particularly in mitigating the effects of algebraic waitingtime distribution, and in giving rise to an exponential-like decay, with a timeconstant, surprisingly, less than the time constant that arises from smallamplitude decay alone.

physical review. e, statistical, nonlinear and soft matter physics

Orientational relaxation in a dispersive dynamic medium : Generalization  of the Kubo-Ivanov-Anderson jump diffusion model to include fractional  environmental dynamics