Distribution of Husimi zeros in polygonal billiards

The zeros of the Husimi function provide a minimal description of individual quantum eigenstates and their distribution is of considerable interest. We provide here a numerical study for pseudointegrable billiards which suggests that the zeros tend to diffuse over phase space in a manner reminiscent of chaotic systems but nevertheless contain a subtle signature of pseudointegrability. We also find that the zeros depend sensitively on the position and momentum uncertainties (Δq and Δp, respectively) with the classical correspondence best when Δq=Δp=√ħ/2. Finally, short-range correlations seem to be well described by the Ginibre ensemble of complex matrices.