TY  - JOUR
A1  - Bodrova, Anna S.
A1  - Chechkin, Aleksei V.
A1  - Cherstvy, Andrey G.
A1  - Metzler, Ralf
T1  - Ultraslow scaled Brownian motion
T2  - New journal of physics : the open-access journal for physics
N2  - We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form D(t) similar or equal to 1/t. For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations.
KW  - anomalous diffusion
KW  - stochastic processes
KW  - ageing
Y1  - 2015
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/38814
SN  - 1367-2630
VL  - 17
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -