Berlin 2008 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 23: Quantum chaos I

DY 23.6: Vortrag

Donnerstag, 28. Februar 2008, 11:00–11:15, MA 001

Algebraic fidelity decay for local perturbations — •Ruven Höhmann, Ulrich Kuhl, and Hans-Jürgen Stöckmann — Fachbereich Physik, Philipps-Universität Marburg, Renthof 5,

From a reflection measurement in a rectangular microwave billiard with an arrangement of randomly distributed scatterers the scattering fidelity was studied with the position of one of the scatterers as the perturbation parameter. Such perturbations have been termed "local" by us since the wave function is influenced only locally [1]. This is in contrast of previous studies of our group where the fidelity decay had been studied as a function of one billiard wall [2]. Using Berry’s random plane wave conjecture, an analytic expression for the fidelity decay due to the shift of one scatterer has been obtained, yielding an algebraic 1/t decay for long times. A perfect agreement between experiment and theory has been obtained, including a predicted scaling behavior concerning the dependence of the fidelity decay on the shift distance. The only free parameter has been determined independently from the variance of the level velocities. From the spectrum the ordinary fidelity amplitude could be determined also, and was found to be in good agreement with the scattering fidelity.
[1] M. Barth, U. Kuhl, and H.-J. Stöckmann, Phys. Rev. Lett. 82, 2026 (1999).
[2] R. Schäfer, H.-J. Stöckmann, T. Gorin, and T. H. Seligman, Phys. Rev. Lett. 95, 184102 (2005).