Dresden 2003 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 52: Quantum chaos II

DY 52.5: Vortrag

Freitag, 28. März 2003, 12:30–12:45, G\"OR/226

Families of orbits in a billiard of constant negative curvature — •Stefan Heusler, Petr Braun, Sebastian Müller und Fritz Haake — Essen university

Following a conjecture of Bohigas, Giannoni and Schmit, the fluctuations in quantum spectra of classically chaotic systems are universal. Although numerically established beyond any doubt, an analytical explanation of that universality is still lacking and is attacked by many groups with semiclassical and field theoretical methods as well as through parametric level dynamics.

We report progress in the semiclassical approach for a special system, the Hadamard-Gutzwiller model. As first found by Sieber and Richter, the distribution of self-crossings and avoided self-crossings of classical orbits in configuration space is crucial. We employ symbolic dynamics for the construction of extremely long periodic orbits without compromising accuracy and for a deeper understanding of the analytic properties of these distributions. The structure of families of periodic orbits contributing to the small-time expansion of the spectral form factor is beginning to shape up.