Dresden 2009 – scientific programme

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CPP: Fachverband Chemische Physik und Polymerphysik

CPP 25: Diffusion and Dynamics

CPP 25.4: Talk

Wednesday, March 25, 2009, 16:15–16:30, ZEU 160

Cluster-resolved scaling theory for particle transport on percolating systems — Axel Kammerer, •Felix Höfling, and Thomas Franosch — Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Fakultät für Physik, Ludwig-Maximilians-Universität München, Germany

A Brownian particle moving between randomly distributed obstacles, a variant of the Lorentz model, constitutes a simple model for transport in heterogeneous environments. Three major transport phenomena are observed: normal diffusion, localization, and anomalous transport. All three aspects may be unified into the concept of transport in a medium with a percolation transition. Recent simulations have revealed that the asymptotic subdiffusive behaviour is only slowly approached and the large corrections cannot be ignored [1].

Thus, it is of general interest to develop a systematic description of universal corrections to scaling in percolating systems [2]. We have derived a new universal exponent relation connecting the leading corrections to scaling of the static cluster structure and of the transport dynamics. The derivation relies on a cluster-resolved scaling theory, unifying the scaling of both the cluster size distribution and the dynamics of a random walker. We have corroborated our scaling theory as well as the exponent relation in detail by large-scale simulations for the square lattice.

[1] Höfling, Franosch, and Frey, Phys. Rev. Lett. 96, 165901 (2006).

[2] Kammerer, Höfling, and Franosch, arXiv:0811.1414, to appear in Europhys. Lett. (2008).