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Microscopic Origin of the Logarithmic Time Evolution of Aging Processes in Complex Systems

Lomholt, Michael A.; Lizana, Ludvig; Metzler, Ralf and Ambjörnsson, Tobias LU (2013) In Physical Review Letters 110(20).
Abstract
There exists compelling experimental evidence in numerous systems for logarithmically slow time evolution, yet its full theoretical understanding remains elusive. We here introduce and study a generic transition process in complex systems, based on nonrenewal, aging waiting times. Each state n of the system follows a local clock initiated at t = 0. The random time tau between clock ticks follows the waiting time density psi (tau). Transitions between states occur only at local clock ticks and are hence triggered by the local forward waiting time, rather than by psi (tau). For power-law forms psi (tau) similar or equal to tau(-1-alpha) (0 < alpha < 1) we obtain a logarithmic time evolution of the state number < n(t)> similar or... (More)
There exists compelling experimental evidence in numerous systems for logarithmically slow time evolution, yet its full theoretical understanding remains elusive. We here introduce and study a generic transition process in complex systems, based on nonrenewal, aging waiting times. Each state n of the system follows a local clock initiated at t = 0. The random time tau between clock ticks follows the waiting time density psi (tau). Transitions between states occur only at local clock ticks and are hence triggered by the local forward waiting time, rather than by psi (tau). For power-law forms psi (tau) similar or equal to tau(-1-alpha) (0 < alpha < 1) we obtain a logarithmic time evolution of the state number < n(t)> similar or equal to log(t/t(0)), while for alpha > 2 the process becomes normal in the sense that < n(t)> similar or equal to t. In the intermediate range 1 < alpha < 2 we find the power-law growth < n(t)> similar or equal to t(alpha-1). Our model provides a universal description for transition dynamics between aging and nonaging states. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review Letters
volume
110
issue
20
publisher
American Physical Society
external identifiers
  • wos:000319064100017
  • scopus:84877801278
ISSN
1079-7114
DOI
10.1103/PhysRevLett.110.208301
language
English
LU publication?
yes
id
2f0054a2-b3e8-49cc-bcc6-ac038b904d5f (old id 3932540)
date added to LUP
2013-07-15 11:09:22
date last changed
2019-09-17 01:37:06
@article{2f0054a2-b3e8-49cc-bcc6-ac038b904d5f,
  abstract     = {There exists compelling experimental evidence in numerous systems for logarithmically slow time evolution, yet its full theoretical understanding remains elusive. We here introduce and study a generic transition process in complex systems, based on nonrenewal, aging waiting times. Each state n of the system follows a local clock initiated at t = 0. The random time tau between clock ticks follows the waiting time density psi (tau). Transitions between states occur only at local clock ticks and are hence triggered by the local forward waiting time, rather than by psi (tau). For power-law forms psi (tau) similar or equal to tau(-1-alpha) (0 &lt; alpha &lt; 1) we obtain a logarithmic time evolution of the state number &lt; n(t)&gt; similar or equal to log(t/t(0)), while for alpha &gt; 2 the process becomes normal in the sense that &lt; n(t)&gt; similar or equal to t. In the intermediate range 1 &lt; alpha &lt; 2 we find the power-law growth &lt; n(t)&gt; similar or equal to t(alpha-1). Our model provides a universal description for transition dynamics between aging and nonaging states.},
  articleno    = {208301},
  author       = {Lomholt, Michael A. and Lizana, Ludvig and Metzler, Ralf and Ambjörnsson, Tobias},
  issn         = {1079-7114},
  language     = {eng},
  number       = {20},
  publisher    = {American Physical Society},
  series       = {Physical Review Letters},
  title        = {Microscopic Origin of the Logarithmic Time Evolution of Aging Processes in Complex Systems},
  url          = {http://dx.doi.org/10.1103/PhysRevLett.110.208301},
  volume       = {110},
  year         = {2013},
}