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.
Cite
@article{arxiv.1407.6630,
title = {Spectral Properties and Dynamical Tunneling in Constant-Width Billiards},
author = {B. Dietz and T. Guhr and B. Gutkin and M. Miski-Oglu and A. Richter},
journal= {arXiv preprint arXiv:1407.6630},
year = {2014}
}