Quantum chaos in one dimension?
  In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest N eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit, N->infinity, the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist. 
Laszlo Ujfalusi, Imre Varga, and Daniel Schumayer
nlin.CD math-ph math.MP quant-ph