Eur. Phys. J. B (2017) 90: 205
https://doi.org/10.1140/epjb/e2017-80270-9

Regular Article

Ageing effects in ultraslow continuous time random walks^★

¹ Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
² Akhiezer Institute for Theoretical Physics, Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine
³ Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany

^a e-mail: achechkin@kipt.kharkov.ua

Received: 9 May 2017
Received in final form: 28 June 2017
Published online: 1 November 2017

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.