2009/10/31 by Vincent Tejedor, Ralf Metzler · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Anomalous diffusion #Computer science #Continuous-time random walk #Diffusion #Diffusion and Search Dynamics #Displacement (psychology) #Ergodicity #Exponent #Fractional Differential Equations Solutions #Gaussian #Jump #Mathematics #Mean squared displacement #Molecular dynamics #Physics #Power law #Quantum mechanics #Random walk #Statistical physics #Statistics #Thermodynamics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1751-8113/43/8/082002
6 pages, 6 figures. Slightly revised version, accepted to J Phys A as a Fast Track Communication
arxiv created 2010/01/25 · openalex publication_date 2010/02/05 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.