title: Spectral properties and dynamical tunneling in constant-width billiards.
abstract: We determine with unprecedented accuracy the lowest 900 eigenvalues of two quantum constant-width billiards from resonance spectra measured with flat, superconducting microwave resonators. While the classical dynamics of the constant-width billiards is unidirectional, a change of the direction of motion is possible in the corresponding quantum system via dynamical tunneling. This becomes manifest in a splitting of the vast majority of resonances into doublets of nearly degenerate ones. The fluctuation properties of the two respective spectra are demonstrated to coincide with those of a random-matrix model for systems with violated time-reversal invariance and a mixed dynamics. Furthermore, we investigate tunneling in terms of the splittings of the doublet partners. On the basis of the random-matrix model we derive an analytical expression for the splitting distribution which is generally applicable to systems exhibiting dynamical tunneling between two regions with (predominantly) chaotic dynamics.
authors.affiliation: Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany.
authors.forename: B
authors.initials: B
authors.lastname: Dietz
authors.affiliation: Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1, D-47048 Duisburg, Germany.
authors.forename: T
authors.initials: T
authors.lastname: Guhr
authors.affiliation: Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1, D-47048 Duisburg, Germany.
authors.forename: B
authors.initials: B
authors.lastname: Gutkin
authors.affiliation: Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany.
authors.forename: M
authors.initials: M
authors.lastname: Miski-Oglu
authors.affiliation: Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany.
authors.forename: A
authors.initials: A
authors.lastname: Richter
mesh_terms: D005583:Fourier Analysis; D008872:Microwaves; D008962:Models, Theoretical; D009038:Motion; D017711:Nonlinear Dynamics; D011789:Quantum Theory; D013057:Spectrum Analysis