TY  - JOUR
A1  - Godec, Aljaz
A1  - Metzler, Ralf
T1  - Finite-Time effects and ultraweak ergodicity breaking in superdiffusive dynamics
T2  - Physical review letters
N2  - We study the ergodic properties of superdiffusive, spatiotemporally coupled Levy walk processes. For trajectories of finite duration, we reveal a distinct scatter of the scaling exponents of the time averaged mean squared displacement (delta x(2)) over bar around the ensemble value 3 - alpha (1 < alpha < 2) ranging from ballistic motion to subdiffusion, in strong contrast to the behavior of subdiffusive processes. In addition we find a significant dependence of the average of (delta x(2)) over bar over an ensemble of trajectories as a function of the finite measurement time. This so-called finite-time amplitude depression and the scatter of the scaling exponent is vital in the quantitative evaluation of superdiffusive processes. Comparing the long time average of the second moment with the ensemble mean squared displacement, these only differ by a constant factor, an ultraweak ergodicity breaking.
Y1  - 2013
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/35268
SN  - 0031-9007
VL  - 110
IS  - 2
PB  - American Physical Society
CY  - College Park
ER  -