Induced superconductivity distinguishes chaotic from integrable   billiards
  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. 
J. A. Melsen, P. W. Brouwer, K. M. Frahm, and C. W. J. Beenakker