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Critical dynamics in systems controlled by fractional kinetic equations


  • Batalov, Lev
  • Batalova, Anastasia


The field theory renormalization group is used for analyzing the fractional Langevin equation with the order of the temporal derivative 0<α<1, fractional Laplacian of the order σ, and Gaussian noise correlator. The case of non-linearity φm with odd m≥3 is considered. It is proved that the model is multiplicatively renormalizable. Propagators were found in the momentum and coordinate representation, expressed in terms of Fox’s H functions.

Suggested Citation

  • Batalov, Lev & Batalova, Anastasia, 2013. "Critical dynamics in systems controlled by fractional kinetic equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 602-611.
  • Handle: RePEc:eee:phsmap:v:392:y:2013:i:4:p:602-611 DOI: 10.1016/j.physa.2012.10.017

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    References listed on IDEAS

    1. Nadarajah, Saralees & Kotz, Samuel, 2006. "On The Product And Ratio Of Gamma And Weibull Random Variables," Econometric Theory, Cambridge University Press, vol. 22(02), pages 338-344, April.
    2. Beck, Christian, 2006. "Stretched exponentials from superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 96-101.
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