Quantal Andreev billiards: Density of states oscillations and the   spectrum-geometry relationship
  Andreev billiards are finite, arbitrarily-shaped, normal-state regions, surrounded by superconductor. At energies below the superconducting energy gap, single-quasiparticle excitations are confined to the normal region and its vicinity, the mechanism for confinement being Andreev reflection. Short-wave quantal properties of these excitations, such as the connection between the density of states and the geometrical shape of the billiard, are addressed via a multiple scattering approach. It is shown that one can, inter alia, hear the stationary chords of Andreev billiards. 
Inanc Adagideli and Paul M. Goldbart (University of Illinois at   Urbana-Champaign)