Microscopic Origin of the Logarithmic Time Evolution of Aging Processes in Complex Systems
(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 powerlaw forms psi (tau) similar or equal to tau(1alpha) (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 powerlaw forms psi (tau) similar or equal to tau(1alpha) (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 powerlaw growth < n(t)> similar or equal to t(alpha1). Our model provides a universal description for transition dynamics between aging and nonaging states. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/3932540
 author
 Lomholt, Michael A.; Lizana, Ludvig; Metzler, Ralf and Ambjörnsson, Tobias ^{LU}
 organization
 publishing date
 2013
 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
 10797114
 DOI
 10.1103/PhysRevLett.110.208301
 language
 English
 LU publication?
 yes
 id
 2f0054a2b3e849ccbcc6ac038b904d5f (old id 3932540)
 date added to LUP
 20130715 11:09:22
 date last changed
 20190917 01:37:06
@article{2f0054a2b3e849ccbcc6ac038b904d5f, 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 powerlaw forms psi (tau) similar or equal to tau(1alpha) (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 powerlaw growth < n(t)> similar or equal to t(alpha1). 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 = {10797114}, 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}, }