Microscopic Origin of the Logarithmic Time Evolution of Aging Processes in Complex Systems
2013 (English)In: Physical Review Letters, ISSN 0031-9007, Vol. 110, no 20, 208301-208306 p.Article in journal, Letter (Refereed) Published
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 τ between clock ticks follows the waiting time density ψ(τ). Transitions between states occur only at local clock ticks and are hence triggered by the local forward waiting time, rather than by ψ(τ). For power-law formsψ(τ)≃τ-1-α (0<α<1) we obtain a logarithmic time evolution of the state number ⟨n(t)⟩≃log(t/t0), while for α>2 the process becomes normal in the sense that ⟨n(t)⟩≃t. In the intermediate range 1<α<2 we find the power-law growth ⟨n(t)⟩≃tα-1. Our model provides a universal description for transition dynamics between aging and nonaging states.
Place, publisher, year, edition, pages
American Physical Society , 2013. Vol. 110, no 20, 208301-208306 p.
Condensed Matter Physics
IdentifiersURN: urn:nbn:se:umu:diva-71381DOI: 10.1103/PhysRevLett.110.208301OAI: oai:DiVA.org:umu-71381DiVA: diva2:623562