To what systems does the Bohigas conjecture apply?

TL;DR

This paper investigates the applicability of the Bohigas conjecture to non-analytic Hamiltonian systems, creating a class of such systems and numerically analyzing their spectral fluctuations.

Contribution

It demonstrates that certain non-analytic Hamiltonian systems can violate the Bohigas conjecture, challenging its universality.

Findings

Spectral fluctuations in the studied systems do not align with the conjecture.

Numerical analysis shows deviations from expected random matrix theory statistics.

The class of Hamiltonians constructed appears to violate the conjecture.

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.