38747
2015
2015
eng
20
28
48
article
IOP Publ. Ltd.
Bristol
1
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Ageing first passage time density in continuous time random walks and quenched energy landscapes
We study the first passage dynamics of an ageing stochastic process in the continuous time random walk (CTRW) framework. In such CTRW processes the test particle performs a random walk, in which successive steps are separated by random waiting times distributed in terms of the waiting time probability density function Psi (t) similar or equal to t(-1-alpha) (0 <= alpha <= 2). An ageing stochastic process is defined by the explicit dependence of its dynamic quantities on the ageing time t(a), the time elapsed between its preparation and the start of the observation. Subdiffusive ageing CTRWs with 0 < alpha < 1 describe systems such as charge carriers in amorphous semiconducters, tracer dispersion in geological and biological systems, or the dynamics of blinking quantum dots. We derive the exact forms of the first passage time density for an ageing subdiffusive CTRW in the semi-infinite, confined, and biased case, finding different scaling regimes for weakly, intermediately, and strongly aged systems: these regimes, with different scaling laws, are also found when the scaling exponent is in the range 1 < alpha < 2, for sufficiently long ta. We compare our results with the ageing motion of a test particle in a quenched energy landscape. We test our theoretical results in the quenched landscape against simulations: only when the bias is strong enough, the correlations from returning to previously visited sites become insignificant and the results approach the ageing CTRW results. With small bias or without bias, the ageing effects disappear and a change in the exponent compared to the case of a completely annealed landscape can be found, reflecting the build-up of correlations in the quenched landscape.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/48/28/285001
1751-8113 (print)
1751-8121 (online)
wos:2015
285001
WOS:000357281400002
Krusemann, H (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland (Suomen Akatemia) within the Finland Distinguished
Professor (FiDiPro) programme
Henning Krüsemann
Aljaz Godec
Ralf Metzler
eng
uncontrolled
first passage
eng
uncontrolled
random walks
eng
uncontrolled
anomalous diffusion
Institut für Physik und Astronomie
Referiert