Random-matrix theory is used to show that the proximity to a superconductor opens a gap in the excitation spectrum of an electron gas confined to a billiard with a chaotic classical dynamics. In contrast, a gapless spectrum is obtained for a non-chaotic rectangular billiard, and it is argued that this is generic for integrable systems.
@article{arxiv.cond-mat/9604058,
title = {Induced superconductivity distinguishes chaotic from integrable billiards},
author = {J. A. Melsen and P. W. Brouwer and K. M. Frahm and C. W. J. Beenakker},
journal= {arXiv preprint arXiv:cond-mat/9604058},
year = {2016}
}