Regensburg 2007 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 27: Quantum chaos III
DY 27.3: Talk
Thursday, March 29, 2007, 11:45–12:00, H2
Semiclassical theory of weak localization in regular billiards: the role of diffractive effects — •Iva Brezinova1, Christoph Stampfer2, Joachim Burgdörfer1, Ludger Wirtz3, and Stefan Rotter1 — 1Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10&136, A-1040 Vienna, Austria, EU — 2Chair of Micro and Nanosystems, Swiss Federal*Institute of Technology Zurich (ETH Zurich), Tannenstr. 3, 8092 Zurich, Switzerland — 3Institute for Electronics, Microelectronics and Nanotechnology, B.P. 60069, 59692 Villeneuve d*Ascq Cedex, France, EU
Weak localization is a quantum interference effect observed in quantum billiards: the conductance through the system is suppressed compared to the classical prediction. Application of a perpendicular magnetic field increases the conductance giving rise to a characteristic dip.
We present a semiclassical theory of weak localization applicable to both regular as well as chaotic quantum billiards. The theory includes pseudo-paths consisting of classical paths joined by diffractive scatterings at the entrance and exit of the billiard. These pseudo-paths connect the classically disjoint path sets of reflected and transmitted paths and thus improve the unitarity of the semiclassical theory. For regular systems we have succeeded in adding up all classical paths as well as the pseudo-paths up to a given length. We compare the semiclassical resistance and conductance with quantum results and find good agreement. We show for a regular system (circular billiard) that the characteristic dip of the conductance as a function of the magnetic field disappears if all non-classical paths are removed.