Hannover 2010 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 21: Poster I

Q 21.69: Poster

Dienstag, 9. März 2010, 16:00–19:00, Lichthof

Multifractality in quantum maps — •John Martin¹, Ignacio Garcia-Mata², Olivier Giraud^3,4, and Bertrand Georgeot^3,4 — ¹Institut de Physique Nucléaire, Atomique et de Spectroscopie, Université de Liège, Bât. B15, B - 4000 Liège, Belgium — ²Departamento de Física, Lab. TANDAR, Comisión Nacional de Energía Atómica, Av. del Libertador 8250, C1429BNP Buenos Aires, Argentina — ³Université de Toulouse, UPS, Laboratoire de Physique Théorique (IRSAMC), F-31062 Toulouse, France — ⁴CNRS, LPT (IRSAMC), F-31062 Toulouse, France

We present our results on the multifractal properties of wave functions for (a) a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics, (b) wave functions at the Anderson transition in the kicked rotator with three incommensurate frequencies (experiments on this system have been performed by Garreau et al.). We perform extensive numerical computations and provide analytical arguments showing that the generalized fractal dimensions are directly related to the parameter of the underlying classical map, and thus to other properties such as spectral statistics.