Cluster-resolved dynamic scaling theory and universal corrections for transport on percolating systems

• Main Authors: Franosch, Thomas, Höfling, Felix
• Other Authors: Ludwig-Maximilians-Universität München, Fakultät für Physik
• Format: Article
• Language: English
• Published: Universitätsbibliothek Leipzig 2015
• Subjects: Diffusion; Transport; diffusion; transport; ddc:530
• Online Access: http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-190406; http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-190406; http://www.qucosa.de/fileadmin/data/qucosa/documents/19040/diff_fund_11%282009%2959.pdf

For a continuum percolation model, it has been shown recentlythat the crossover from pure subdiffusion to normal diffusion extends over five decades in time [1, 2]; in addition, the asymptotic behavior is slowly approached and the large corrections cannot simply be ignored. Thus, it is of general interest to develop a systematic description of universal corrections to scaling in percolating systems. For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behavior at criticality. Our derivation is based on a cluster-resolved scaling theory unifying the scaling of both the cluster size distribution and the dynamics of a random walker. We corroborate our theoretical approach by extensive simulations for a site percolating square lattice and numerically determine both the static and dynamic correction exponents [3].