2014/06/26 by Aljaž Godec, Aljaz Godec, Aleksei V. Chechkin +4
Computer Science · Mathematics · Physics and Astronomy · #Diffusion #Fractional Differential Equations Solutions #Nonlinear Dynamics and Pattern Formation #Physics #Statistical physics #Thermodynamics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1751-8113/47/49/492002
published as J. Phys. A 47, 492002 (2014) Fast Track Communication · 5 pages, 6 figures, RevTeX
arxiv created 2014/06/26 · openalex publication_date 2014/11/14 · arxiv updated 2014/12/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) ⟨ x2(t)⟩≃logγt. Comparison of annealed continuous time random walks (CTRWs) with logarithmic waiting time distribution ψ(τ)≃1/(τlog1+γτ) and Sinai diffusion in quenched random landscapes shows striking similarities, despite their very different physical nature. In particular, they exhibit a weakly non-ergodic disparity of the time and ensemble averaged MSDs. Remarkably, for the CTRW we observe that the fluctuations of time averages become universal with an exponential suppression of mobile trajectories. We discuss the fundamental connection between the Golosov localization effect and non-ergodicity in the sense of the disparity between ensemble and time averaged MSD.