Subordination model of anomalous diffusion leading to the two-power-law relaxation responses

Details Subordination model of anomalous diffusion leading to the two-power-law relaxation responses Subordination model of anomalous diffusion leading to the two-power-law relaxation responses

2011-11-13

arxiv.org/abs/1111.3014v1

EPL 91, 40003 (2010)

Physics

Condensed Matter

Statistical Mechanics

5 pages; 3 figures; corrected version

Scientific paper

10.1209/0295-5075/91/40003

We derive a general pattern of the nonexponential, two-power-law relaxation from the compound subordination theory of random processes applied to anomalous diffusion. The subordination approach is based on a coupling between the very large jumps in physical and operational times. It allows one to govern a scaling for small and large times independently. Here we obtain explicitly the relaxation function, the kinetic equation and the susceptibility expression applicable to the range of experimentally observed power-law exponents which cannot be interpreted by means of the commonly known Havriliak-Negami fitting function. We present a novel two-power relaxation law for this range in a convenient frequency-domain form and show its relationship to the Havriliak-Negami one.

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