Johannes Schulz, Eli Barkai, Ralf Metzler
We study time averages of single particle trajectories in scale free anomalous diffusion processes, in which the measurement starts at some time t_a>0 after initiation of the process at the time origin, t=0. Using ageing renewal theory we show that for such non-stationary processes a large class of observables are affected by a unique ageing function, which is independent of boundary conditions or the external forces. We quantify the weakly non-ergodic nature of this process in terms of the distribution of time averages and the ergodicity breaking parameter which both explicitly depend on the ageing time t_a. Consequences for the interpretation of single particle tracking data are discussed.
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http://arxiv.org/abs/1204.0878
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