Regensburg 2013 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
DY: Fachverband Dynamik und Statistische Physik
DY 26: Quantum Chaos I
DY 26.2: Vortrag
Donnerstag, 14. März 2013, 10:00–10:15, H47
Universality in chaotic quantum transport: The concordance between random matrix and semiclassical theories — Gregory Berkolaiko1 and •Jack Kuipers2 — 1Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA — 2Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the classical scattering trajectories. Correlations between such trajectories can be organized diagrammatically and have been shown to yield universal answers for some observables. Here, we develop the general combinatorial treatment of the semiclassical diagrams, through a connection to factorizations of permutations. We show agreement between the semiclassical and random matrix approaches to the moments of the transmission eigenvalues. The result is valid for all moments to all orders of the expansion in inverse channel number for all three main symmetry classes (with and without time reversal symmetry and spin-orbit interaction) and extends to nonlinear statistics. This finally explains the applicability of random matrix theory to chaotic quantum transport in terms of the underlying dynamics as well as providing semiclassical access to the probability density of the transmission eigenvalues.
Phys. Rev. E 85 (2012) 045201