1211.1539 (Daniela Froemberg et al.)

Fluctuations of time averaged diffusivities for the Lévy walk    [PDF]

Daniela Froemberg, Eli Barkai

The L\'evy walk model is a stochastic framework of enhanced diffusion with many applications in physics and biology. Here we investigate the time averaged mean squared displacement $\bar{\delta^2}$ often used to analyze single particle tracking experiments. The ballistic phase of the motion is non-ergodic and we obtain analytical expressions for the fluctuations of $\bar{\delta^2}$. For enhanced sub-ballistic diffusion we observe numerically apparent ergodicity breaking on long time scales. As observed by Akimoto Phys. Rev. Lett. 108, 164101 (2012) deviations of temporal averages $\bar{\delta^2}$ from the ensemble average $$ depend on the initial preparation of the system, and here we quantify this discrepancy from normal diffusive behavior.

View original: http://arxiv.org/abs/1211.1539