Experimental Evidence of the Role of Compound Counting Processes in Random Walk Approaches to Fractional Dynamics

Details Experimental Evidence of the Role of Compound Counting Processes in Random Walk Approaches to Fractional Dynamics Experimental Evidence of the Role of Compound Counting Processes in Random Walk Approaches to Fractional Dynamics

2011-11-13

arxiv.org/abs/1111.3030v1

Phys. Rev. E 83, 051102 (2011)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 5 figures; corrected version

Scientific paper

10.1103/PhysRevE.83.051102

We present dielectric spectroscopy data obtained for gallium-doped Cd$_{0.99}$Mn$_{0.01}$Te:Ga mixed crystals which exhibit a very special case of the two-power-law relaxation pattern with the high-frequency power-law exponent equal to 1. We explain this behavior, which cannot be fitted by none of the well-known empirical relaxation functions, in a subordinated diffusive framework. We propose diffusion scenario based on a renormalized clustering of random number of spatio-temporal steps in the continuous time random walk. Such a construction substitutes the renewal counting process, used in the classical continuous time random walk methodology, by a compound counting one. As a result, we obtain a novel relaxation function governing the observed non-standard pattern, and we show the importance of the compound counting processes in studying fractional dynamics of complex systems.

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