TY  - JOUR
A1  - Safdari, Hadiseh
A1  - Chechkin, Aleksei V.
A1  - Jafari, Gholamreza R.
A1  - Metzler, Ralf
T1  - Aging scaled Brownian motion
T2  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - 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.
Y1  - 2015
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/39007
SN  - 1539-3755
SN  - 1550-2376
VL  - 91
IS  - 4
PB  - American Physical Society
CY  - College Park
ER  -