Localization and universal fluctuations in ultraslow diffusion processes

Abstract

We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) $⟨x^2(t)⟩\simeq {\log }^{\gamma }t$. Comparison of annealed continuous time random walks (CTRWs) with logarithmic waiting time distribution $\psi (\tau )\simeq 1/(\tau {\log }^{1+\gamma }\tau )$ 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.

5 pages, 6 figures, RevTeX

References in corpus (9)

• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Weakly non-ergodic Statistical Physics
• Universal fluctuations in subdiffusive transport
• Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder
• Helix or Coil? Fate of a Melting Heteropolymer
• Continuous-time random walk with a superheavy-tailed distribution of waiting times
• Aging processes in systems with anomalous slow dynamics
• DNA unzipping and the unbinding of directed polymers in a random media

Cited by in corpus (8)

• Ageing underdamped scaled Brownian motion: ensemble and time averaged particle displacements, non-ergodicity, and the failure of the overdamping approximation
• First passage time statistics for two-channel diffusion
• Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes
• Optimization and universality of Brownian search in quenched heterogeneous media
• Persistent Sinai type diffusion in Gaussian random potentials with decaying spatial correlations
• Inhomogeneous diffusion and ergodicity breaking induced by global memory effects
• Non-stationary Markovian Replication Process causing Diverse Diffusions
• Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion