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Ageing effects in ultraslow continuous time random walks

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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.

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Authors and Affiliations

  1. Institute of Physics and Astronomy, University of Potsdam, 14476, Potsdam, Germany

    Aleksei V. Chechkin & Ralf Metzler

  2. Akhiezer Institute for Theoretical Physics, Kharkov Institute of Physics and Technology, Kharkov, 61108, Ukraine

    Aleksei V. Chechkin

  3. Max Planck Institute for the Physics of Complex Systems, 01187, Dresden, Germany

    Holger Kantz

Authors
  1. Aleksei V. Chechkin
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  2. Holger Kantz
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Correspondence to Aleksei V. Chechkin.

Additional information

Contribution to the Topical Issue “Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook”, edited by Ryszard Kutner and Jaume Masoliver.

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Chechkin, A.V., Kantz, H. & Metzler, R. Ageing effects in ultraslow continuous time random walks. Eur. Phys. J. B 90, 205 (2017). https://doi.org/10.1140/epjb/e2017-80270-9

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