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DY: Dynamik und Statistische Physik

DY 15: Quantum Chaos

DY 15.4: Vortrag

Montag, 27. März 2006, 15:45–16:00, SCH 251

Spectral properties of mushroom billiards — •Thomas Friedrich — Schlossgartenstraße 9, 64289 Darmstadt

In 2001 Bunimovich proposed a family of billiards shaped like mushrooms as a generalization of the well studied stadium billiard. The classical phase space of mushroom billiards is well separated into regular and chaotic regions with no KAM islands. We investigated the quantum properties of mushroom billiards experimentally using superconducting microwave cavities by measuring frequency spectra and wave functions. In the measured spectra a supershell structure was observed which, as could be shown, is due to the interference of short periodic orbits of comparable length. Their influences become also visible in the nearest neighbour distance distribution of resonance frequencies. We succeeded in separating the eigenmodes of the mushroom billiard into regular and chaotic modes following Poissonian and GOE statistics, respectively. With those subsets of modes dynamic tunneling between the two phase space regions was observed in terms of field distributions and frequency shifts. We thus found that the spectral properties of mushroom billiards are mainly governed by shell structures and dynamic tunneling.

This work has been supported by DFG within SFB 634.