Chaotic Signatures in the Spectrum of a Quantum Double Well
  The spectrum of a double well constructed of a square barrier embedded in an infinite well is analyzed. Level statistics for levels slightly above the barrier show signs of Wigner statistics usually associated with quantum chaos. The correspondence with Wigner statistics improves when an ensemble of systems with slightly different barrier heights is taken, possibly reflecting an adiabatic time-dependent modulation of the barrier. 
R. Berkovits, Y. Ashkenazy, L. P. Horwitz and J. Levitan