On the distribution of zeros of chaotic wavefunctions

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Abstract
Wavefunctions in a phase-space representation can be expressed as entire functions of their zeros if the phase space is compact. These zeros seem to hide a lot of relevant and explicit information about the underlying classical dynamics. Besides, an understanding of their statistical properties may prove to be useful in the analytical calculations of the wavefunctions in quantum-chaotic systems. This motivates us to pursue the present study which by a numerical statistical analysis shows that both long-range correlations as well as short-range correlations exist between zeros; while the latter turn out to be universal and parametric independent, the former seem to be system dependent and are significantly affected by various parameters, i.e. symmetry, localization, etc. Furthermore, for the delocalized quantum dynamics, the distribution of these zeros seem to mimic that of the zeros of the random functions as well as random polynomials.
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