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Ageing effects in ultraslow continuous time random walks

Author

Listed:
  • Aleksei V. Chechkin

    (Institute of Physics and Astronomy, University of Potsdam
    Akhiezer Institute for Theoretical Physics, Kharkov Institute of Physics and Technology)

  • Holger Kantz

    (Max Planck Institute for the Physics of Complex Systems)

  • Ralf Metzler

    (Institute of Physics and Astronomy, University of Potsdam)

Abstract

In ageing systems physical observables explicitly depend on the time span elapsing between the original initiation of the system and the actual start of the recording of the particle motion. We here study the signatures of ageing in the framework of ultraslow continuous time random walk processes with super-heavy tailed waiting time densities. We derive the density for the forward or recurrent waiting time of the motion as function of the ageing time, generalise the Montroll–Weiss equation for this process, and analyse the ageing behaviour of the ensemble and time averaged mean squared displacements.

Suggested Citation

  • Aleksei V. Chechkin & Holger Kantz & Ralf Metzler, 2017. "Ageing effects in ultraslow continuous time random walks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(11), pages 1-12, November.
    • Handle: RePEc:spr:eurphb:v:90:y:2017:i:11:d:10.1140_epjb_e2017-80270-9
    DOI: 10.1140/epjb/e2017-80270-9
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