Your browser has javascript turned off or blocked. This will lead to some parts of our website to not work properly or at all. Turn on javascript for best performance.

The browser you are using is not supported by this website. All versions of Internet Explorer are no longer supported, either by us or Microsoft (read more here: https://www.microsoft.com/en-us/microsoft-365/windows/end-of-ie-support).

Please use a modern browser to fully experience our website, such as the newest versions of Edge, Chrome, Firefox or Safari etc.

Face of Tobias Ambjörnsson. Photo.

Tobias Ambjörnsson

Senior lecturer

Face of Tobias Ambjörnsson. Photo.

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

Author

  • Michael A. Lomholt
  • Ludvig Lizana
  • Ralf Metzler
  • Tobias Ambjörnsson

Summary, in English

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.

Department/s

  • Computational Biology and Biological Physics

Publishing year

2013

Language

English

Publication/Series

Physical Review Letters

Volume

110

Issue

20

Document type

Journal article

Publisher

American Physical Society

Topic

  • Biophysics

Status

Published

ISBN/ISSN/Other

  • ISSN: 1079-7114