Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2007-12-14
J. Chem. Phys. 128, 164517 (2008)
Physics
Condensed Matter
Soft Condensed Matter
14 pages
Scientific paper
10.1063/1.2901170
The dynamic properties of a classical tracer particle in a random, disordered medium are investigated close to the localization transition. For Lorentz models obeying Newtonian and diffusive motion at the microscale, we have performed large-scale computer simulations, demonstrating that universality holds at long times in the immediate vicinity of the transition. The scaling function describing the crossover from anomalous transport to diffusive motion is found to vary extremely slowly and spans at least 5 decades in time. To extract the scaling function, one has to allow for the leading universal corrections to scaling. Our findings suggest that apparent power laws with varying exponents generically occur and dominate experimentally accessible time windows as soon as the heterogeneities cover a decade in length scale. We extract the divergent length scales, quantify the spatial heterogeneities in terms of the non-Gaussian parameter, and corroborate our results by a thorough finite-size analysis.
Franosch Thomas
Frey Erwin
Höfling Felix
Munk Tobias
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