Berlin 2015 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 3: Anomalous Diffusion (joint session DY/ CPP)
DY 3.1: Vortrag
Montag, 16. März 2015, 09:30–09:45, BH-N 334
Anomalous diffusion in corrugated potentials with spatial correlations: faster than normal, and other surprises — •Igor Goychuk — Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany
Normal diffusion in corrugated potentials with spatially
uncorrelated Gaussian energy
disorder famously explains the origin of non-Arrhenius exp[−σ2/(kBT)2]
temperature-dependence in
disordered systems. We show [1] 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 σ∼ 4−5 kBT.
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 kBT,
or merely 0.05−0.075 eV.
[1] I. Goychuk and V. Kharchenko, Phys. Rev. Lett. 113, 100601 (2014).