title: Microscopic origin of the logarithmic time evolution of aging processes in complex systems.
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 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 forms ψ(τ) ≃ τ(-1-α) (0 < α < 1) we obtain a logarithmic time evolution of the state number ⟨n(t)⟩ ≃ log(t/t(0)), 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)⟩ ≃ t(α-1). Our model provides a universal description for transition dynamics between aging and nonaging states.
authors.affiliation: MEMPHYS, Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark.
authors.forename: Michael A
authors.initials: MA
authors.lastname: Lomholt
authors.affiliation: Department of Physics and Center for Soft Matter Research, New York University, 4 Washington Place, New York, New York 10003, USA and Department of Physics, Integrated Science Lab, Umeå University, SE-901 87 Umeå, Sweden.
authors.forename: Ludvig
authors.initials: L
authors.lastname: Lizana
authors.affiliation: Institute for Physics and Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany and Department of Physics, Tampere University of Technology, FI-33101 Tampere, Finland.
authors.forename: Ralf
authors.initials: R
authors.lastname: Metzler
authors.affiliation: Department of Astronomy and Theoretical Physics, Lund University, SE-22362 Lund, Sweden.
authors.forename: Tobias
authors.initials: T
authors.lastname: Ambjörnsson
mesh_terms: D004247:DNA / Q000737:chemistry; D008962:Models, Theoretical; D013997:Time Factors
chemical_list: D004247:DNA