Berlin 2005 – scientific programme

Parts | Days | Selection | Search | Downloads | Help

SYRS: Renormalization and Scaling

SYRS 1: SYRS I

SYRS 1.3: Invited Talk

Saturday, March 5, 2005, 09:30–10:00, TU H3010

Transport properties of percolation clusters — •Olaf Stenull — Fachbereich Physik, Universitaet Duisburg-Essen, Campus Essen, 45117 Essen

Percolation is one of the most prominent problems in statistical physics. Theoretical studies of percolation and the application of percolation models in diverse scientific disciplines have resulted in thousands of papers over the last decades. The talk focuses on the electric transport properties of isotropic and directed percolation clusters as explained by the renormalization group. For studying these properties we consider simple and intuitive models, viz. the random resistor network, a bond percolation model where open bonds function as insulators and occupied bonds function as resistors, and the random diode network, where occupied bonds function as diodes. We explain the field theoretic formulation of these models and sketch their diagrammatic perturbation theory. It turns out that the Feynman diagrams for these models can be interpreted as if they were real networks: they consist of insulators and respectively resistors or diodes, they carry currents and so on. Being interested in a certain property of a real network we essentially just have to determine the corresponding property of the Feynman diagrams. For example, the resistance of the Feynman diagrams provides us with the average resistance of the real networks etc. We review some of the results obtained by exploiting this real world interpretation and compare them to numerical results.