To what systems does the Bohigas conjecture apply?

Abstract

We test the applicability of the Bohigas conjecture to systems whose Hamiltonian is not written as a closed form analytic expression. A class of such Hamiltonians is created and appear to violate the conjecture. Numerical methods are employed to find the spectra of a two-dimensional, classically chaotic "billiard" system whose Hamiltonian is in this class. We find that the spectral fluctuations are not in agreement with the conjecture.