TY  - JOUR
A1  - Cherstvy, Andrey G.
A1  - Metzler, Ralf
T1  - Ergodicity breaking, ageing, and confinement in generalized diffusion processes with position and time dependent diffusivity
T2  - Journal of statistical mechanics: theory and experiment
N2  - We study generalized anomalous diffusion processes whose diffusion coefficient D(x, t) similar to D-0x(alpha)t(beta) depends on both the position x of the test particle and the process time t. This process thus combines the features of scaled Brownian motion and heterogeneous diffusion parent processes. We compute the ensemble and time averaged mean squared displacements of this generalized diffusion process. The scaling exponent of the ensemble averaged mean squared displacement is shown to be the product of the critical exponents of the parent processes, and describes both subdiffusive and superdiffusive systems. We quantify the amplitude fluctuations of the time averaged mean squared displacement as function of the length of the time series and the lag time. In particular, we observe a weak ergodicity breaking of this generalized diffusion process: even in the long time limit the ensemble and time averaged mean squared displacements are strictly disparate. When we start to observe this process some time after its initiation we observe distinct features of ageing. We derive a universal ageing factor for the time averaged mean squared displacement containing all information on the ageing time and the measurement time. External confinement is shown to alter the magnitudes and statistics of the ensemble and time averaged mean squared displacements.
KW  - diffusion
Y1  - 2015
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/38953
SN  - 1742-5468
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -