Anomalous features of diffusion in corrugated potentials with spatial correlations: faster than normal, and other surprises

Abstract

Normal diffusion in corrugated potentials with spatially uncorrelated Gaussian energy disorder famously explains the origin of non-Arrhenius $\exp [-{\sigma }^2/(k_B{T}^2)]$ temperature-dependence in disordered systems. Here we show that unbiased diffusion remains asymptotically normal also in the presence of spatial correlations decaying to zero. However, due to a temporal lack of self-averaging transient subdiffusion emerges on mesoscale, and it can readily reach macroscale even for moderately strong disorder fluctuations of $\sigma \sim 4-5k_{B}T$. Due to its nonergodic origin such subdiffusion exhibits a large scatter in single trajectory averages. However, at odds with intuition, it occurs essentially faster than one expects from the normal diffusion in the absence of correlations. We apply these results to diffusion of regulatory proteins on DNA molecules and predict that such diffusion should be anomalous, but much faster than earlier expected on a typical length of genes for a realistic energy disorder of several room $k_{B}T$, or merely $0.05-0.075$ eV.

References in corpus (4)

• Random Time-Scale Invariant Diffusion and Transport Coefficients
• The long reach of DNA sequence heterogeneity in diffusive processes
• Occupation Time Statistics in the Quenched Trap Model
• Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder

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• Non-stationary Markovian Replication Process causing Diverse Diffusions