Year: 2013
Type: article
Abstract: 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 $\overline{{\ensuremath{\delta}}^{2}}$ often used to analyze single particle tracking experiments. The ballistic phase of the motion is nonergodic and we obtain analytical expressions for the fluctuations of $\overline{{\ensuremath{\delta}}^{2}}$. For enhanced subballistic 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 $\overline{{\ensuremath{\delta}}^{2}}$ from the ensemble average $\ensuremath{\langle}{x}^{2}\ensuremath{\rangle}$ depend on the initial preparation of the system, and here we quantify this discrepancy from normal diffusive behavior. Time-averaged response to a bias is considered and the resultant generalized Einstein relations are discussed.
Source: Physical Review E
Authors: D. Froemberg, E. Barkai
Institution: Bar-Ilan University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2335469162