Splitting of the Universality Class of Anomalous Transport in Crowded Media

by Thomas Franosch (Institut für Theoretische Physik, Universität Innsbruck, Austria)

Tuesday 14 Mar 2017, 14:30 → 15:15 Europe/Rome

Aula 5 (Dip. di Fisica - Edificio E. Fermi)

The basic paradigm of complex transport in disordered structures has been formulated originally by H.A. Lorentz as the motion of a tracer particle in a random structure of arrested scatterers. A striking prediction is the emergence of subdiffusive motion, concomitantly, the model exhibits a localization transition which has also been found in fluids confined to porous host structures and, at intermediate time scales, also in nanoporous silica melts or in size-disparate mixtures.  The localization transition is driven by a continuum percolation transition of the underlying geometry. Upon increasing the excluded volume, the spanning cluster in the accessible space is diluted until, at a critical excluded volume fraction, it becomes a fractal structure and the mean-square displacement of a tracer on the critical spanning cluster becomes anomalous. While for structural properties, lattice and continuum percolation belong to the same universality class, the dynamic universality class describing transport splits, since in the case of continuum percolation long-range transport depends on the passage through arbitrarily narrow channels.  In this talk we provide an overview of the physics of the Lorentz model, in particular, we relax idealizing assumptions of the Lorentz model to investigate the robustness of the critical dynamics near the localization transition. First, we introduce obstacle correlations by using frozen-in hard-sphere fluids as realistic host structures, thereby changing the statistics of channel widths for the tracer particle. Second, we gradually change the microscopic dynamics from ballistic to Brownian which affects the rules how narrow channels in the system are probed. Our results confirm that the microscopic dynamics can dominate the relaxational behavior even at long times in striking contrast to glassy dynamics.  If time permits I will also report on an application of the Lorentz model in terms of magneto-transport. Here we report on a delocalization transition induced by skipping orbits along the perimeter of a percolating cluster.