Anomalous diffusion in correlated continuous time random walks

We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with the mean squared displacement ⟨ r 2 ( t )⟩ ≃ t 2/3 . Long-ranged correlations of the waiting times with a power-law exponent α (0 < α ⩽ 2) give rise to subdiffusion of the form ⟨ r 2 ( t )⟩ ≃ t α/(1 + α) . In contrast, correlations in the jump lengths are shown to produce superdiffusion. We show that in both cases weak ergodicity breaking occurs. Our results are in excellent agreement with simulations.