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Experimental evidence of the role of compound counting processes in random walk approaches to fractional dynamics

Justyna Trzmiel* and Karina Weron†

Aleksander Stanislavsky‡

Agnieszka Jurlewicz§

  • Institute of Physics, Wrocław University of Technology,Wyb.Wyspiańskiego 27, PL-50–370 Wrocław, Poland

  • Institute of Radio Astronomy, 4 Chervonopraporna Street, 61002 Kharkov, Ukraine

  • Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wrocław University of Technology, Wyb.Wyspiańskiego 27, PL-50–370 Wrocław, Poland

  • *justyna.trzmiel@pwr.wroc.pl
  • †Karina.Weron@pwr.wroc.pl
  • ‡alexstan@ri.kharkov.ua
  • §Agnieszka.Jurlewicz@pwr.wroc.pl
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Phys. Rev. E 83, 051102 – Published 2 May, 2011Erratum Phys. Rev. E 83, 059908 (2011)

DOI: https://doi.org/10.1103/PhysRevE.83.051102

Abstract

We present dielectric spectroscopy data obtained for gallium-doped Cd0.99Mn0.01Te: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 any of the well-known empirical relaxation functions, in a subordinated diffusive framework. We propose a diffusion scenario based on a renormalized clustering of a random number of spatio-temporal steps in the continuous-time random walk. Such a construction substitutes the renewal counting process, which is used in the classical continuous time random walk methodology, with a compound counting one. As a result, we obtain an appropriate relaxation function governing the observed nonstandard pattern, and we show the importance of the compound counting processes in studying fractional dynamics of complex systems.

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      Corrections

      23 May, 2011

      Erratum

      Publisher’s Note: Experimental evidence of the role of compound counting processes in random walk approaches to fractional dynamics [Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.83.051102 83, 051102 (2011)]

      Justyna Trzmiel, Karina Weron, Aleksander Stanislavsky, and Agnieszka Jurlewicz
      Phys. Rev. E 83, 059908 (2011)

      Article Text

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      Information

      Phys. Rev. E 83, 051102– Published 2 May, 2011
      • Received 7 February 2011
      • Corrected 23 May 2011

      ©2011 American Physical Society

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