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Non-renewal counting processes in systems with ageing waiting times: microscopic origin of logarithmic time evolution | | Michael A. Lomholt
; Tobias Ambjornsson
; Ludvig Lizana
; Ralf Metzler
; | | Date: |
7 Aug 2012 | | Abstract: | We study a generic counting process for systems governed by ageing waiting
times. In contrast to renewal continuous time random walks with independent
waiting times, we consider the case when each state is characterized by its own
internal waiting time process, having been initiated at time t=0. Therefore
each transition from state n to n+1 is triggered by psi_1, the forward waiting
time density, instead of the regular waiting time density psi. For states
characterized by heavy-tailed forms of psi we obtain an asymptotically
logarithmic evolution of the counting dynamics n(t), whose fluctuations vanish
relatively to the mean. The counting process introduced here describes the
dynamics of crack propagation, the counting of on-off transitions in ensembles
of blinking quantum dots, or, more generally, the dynamics in complex systems
such as glasses or biological cells. | | Source: | arXiv, 1208.1383 | | Services: | Forum | Review | PDF | Favorites | |
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