Distribution of Husimi Zeroes in Polygonal Billiards

The zeroes 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 pseudo- integrable billiards which suggests that the zeroes tend to diffuse over phase space in a manner reminiscent of chaotic systems but nevertheless contain a subtle signature of pseudo-integrability. We also find that the zeroes depend sensitively on the position and momentum uncertainties with the classical correspondence best when the position and momentum uncertainties are equal. Finally, short range correlations seem to be well described by the Ginibre ensemble of complex matrices.