ON THE DISTRIBUTION OF ZEROS OF CHAOTIC WAVE-FUNCTIONS

Wavefunctions in a phase-space representation can be expressed as enti re functions of their zeros if the phase space is compact. These zeros seem to hide a lot of relevant and explicit information about the und erlying classical dynamics. Besides, an understanding of their statist ical 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 sho ws that both long-range correlations as well as short-range correlatio ns 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, localiza tion, etc. Furthermore, for the delocalized quantum dynamics, the dist ribution of these zeros seem to mimic that of the zeros of the random functions as well as random polynomials.