Persistent Sinai type diffusion in Gaussian random potentials with decaying spatial correlations

Abstract

Logarithmic or Sinai type subdiffusion is usually associated with random force disorder and non-stationary potential fluctuations whose root mean squared amplitude grows with distance. We show here that extremely persistent, macroscopic ultraslow logarithmic diffusion also universally emerges at sufficiently low temperatures in stationary Gaussian random potentials with spatially decaying correlations, known to exist in a broad range of physical systems. Combining results from extensive simulations with a scaling approach we elucidate the physical mechanism of this unusual subdiffusion. In particular, we explain why with growing temperature and/or time a first crossover occurs to standard, power-law subdiffusion, with a time-dependent power law exponent, and then a second crossover occurs to normal diffusion with a disorder-renormalized diffusion coefficient. Interestingly, the initial, nominally ultraslow diffusion turns out to be much faster than the universal de Gennes-Baessler-Zwanzig limit of the renormalized normal diffusion, which physically cannot be attained at sufficiently low temperatures and/or for strong disorder. The ultraslow diffusion is also non-ergodic and displays a local bias phenomenon. Our simple scaling theory not only explains our numerical findings, but qualitatively has also a predictive character.

References in corpus (16)

• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Stochastic Ergodicity Breaking: a Random Walk Approach
• Physical Constraints and Functional Characteristics of Transcription Factor-DNA Interaction
• Random Walkers in 1-D Random Environments: Exact Renormalization Group Analysis
• The long reach of DNA sequence heterogeneity in diffusive processes
• Weak disorder: anomalous transport and diffusion are normal yet again
• Searching fast for a target on a DNA without falling to traps
• Occupation Time Statistics in the Quenched Trap Model
• Colloids in light fields: particle dynamics in random and periodic energy landscapes
• Anomalous features of diffusion in corrugated potentials with spatial correlations: faster than normal, and other surprises
• Localization and universal fluctuations in ultraslow diffusion processes
• Universal fluctuations in subdiffusive transport
• Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder
• Brownian particles on rough substrates: Relation between the intermediate subdiffusion and the asymptotic long-time diffusion
• Experimental creation and characterization of random potential energy landscapes exploiting speckle patterns
• Real sequence effects on the search dynamics of transcription factors on DNA

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