UNIVERSAL FLUCTUATIONS OF ZEROS OF CHAOTIC WAVE-FUNCTIONS

Wavefunctions of one and two-dimensional quantum systems can be parame trized by a finite number of zeros lying in phase space. We study corr elations of these zeros for fully chaotic systems in terms of a statis tical model based on random polynomials. Excellent agreement is found for the two-point correlation function and nearest-neighbour spacing d istribution of this model and the results obtained for wavefunctions o f dynamical systems. We conjecture that these correlation functions ar e valid for any chaotic system after rescaling the phase-space distanc es (unfolding). Some consequences for the distribution of zeros due to time-reversal symmetry are also discussed.