title: Aging scaled Brownian motion.
abstract: Scaled Brownian motion (SBM) is widely used to model anomalous diffusion of passive tracers in complex and biological systems. It is a highly nonstationary process governed by the Langevin equation for Brownian motion, however, with a power-law time dependence of the noise strength. Here we study the aging properties of SBM for both unconfined and confined motion. Specifically, we derive the ensemble and time averaged mean squared displacements and analyze their behavior in the regimes of weak, intermediate, and strong aging. A very rich behavior is revealed for confined aging SBM depending on different aging times and whether the process is sub- or superdiffusive. We demonstrate that the information on the aging factorizes with respect to the lag time and exhibits a functional form that is identical to the aging behavior of scale-free continuous time random walk processes. While SBM exhibits a disparity between ensemble and time averaged observables and is thus weakly nonergodic, strong aging is shown to effect a convergence of the ensemble and time averaged mean squared displacement. Finally, we derive the density of first passage times in the semi-infinite domain that features a crossover defined by the aging time.
authors.affiliation: Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran.|Institute of Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany.
authors.forename: Hadiseh
authors.initials: H
authors.lastname: Safdari
authors.affiliation: Institute of Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany.|Institute for Theoretical Physics, Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine.|Max-Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany.
authors.forename: Aleksei V
authors.initials: AV
authors.lastname: Chechkin
authors.affiliation: Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran.
authors.forename: Gholamreza R
authors.initials: GR
authors.lastname: Jafari
authors.affiliation: Institute of Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany.|Department of Physics, Tampere University of Technology, FI-33101 Tampere, Finland.
authors.forename: Ralf
authors.initials: R
authors.lastname: Metzler