Berlin 2008 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 17: Poster I
DY 17.4: Poster
Tuesday, February 26, 2008, 16:00–18:00, Poster C
The random phase hypothesis and the circular ensembles — •Rudolf A. Roemer1 and Hermann Schulz-Baldes2 — 1Department of Physics and Centre for Scientific Computing, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK — 2Institut für Mathematik, Universität Erlangen-Nürnberg, Bismarkstrasse 1 1/2, 91054 Erlangen, Deutschland
A new type of a random phase hypothesis for multi-channel disordered wires is presented, stating that the random action of the symplectic transfer matrices on the Lagrangian planes has an isotropic invariant measure on the elliptic channels of the wire. When the Lagrangian planes are identified with the unitary matrices via the stereographic projection, these isotropic invariant measures become precisely those of Dyson’s circular ensembles. This is numerically shown to hold at weak disorder regime in both metallic and localized regime of various physical models belonging to different universality classes.