Figure 1

Numerical results for the probability distribution function for subdiffusion (top left, $\alpha =0.5$), normal diffusion (top right, $\alpha =1$) and superdiffusion (bottom, $\alpha =1.5$). The time averages (circles) are obtained by following one particle trajectory and calculating the histogram for times from $t=100$ to $t=5000$. For the ensemble averages (squares), we calculate the histogram using $5\times {10}^4$ particles, at time $t=1000$. The continuous line is the Maxwell-Boltzmann distribution. Insets: Curves $a$ correspond to the functions $t^{\alpha }$ and curves $b$ to the simulated mean square displacements.Reuse & Permissions