Distribution of zeros of the Husimi function in systems with degeneracy

The distribution of zeros of the Husimi function of energy eigenstates has proven to be a very useful tool for the characterization of the quantum transition from order to chaos in systems without degeneracy. In this paper, we show, by means of calculations on the Henon-Heiles Hamiltonian system, that the quantum order-chaos transition in systems with degeneracy can also be characterized through the distribution of the Husimi function zeros, providing that the appropriate linear combination of degenerate eigenstates is used. If using an arbitrary linear combination, spurious results can be achieved, suggesting a wrong premature quantum transition to chaos.