Universal fluctuations of zeros of chaotic wavefunctions

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Abstract
Wavefunctions of one and two-dimensional quantum systems can be parametrized by a finite number of zeros lying in phase space. We study correlations of these zeros for fully chaotic systems in terms of a statistical model based on random polynomials. Excellent agreement is found for the two-point correlation function and nearest-neighbour spacing distribution of this model and the results obtained for wavefunctions of dynamical systems. We conjecture that these correlation functions are valid for any chaotic system after rescaling the phase-space distances (unfolding). Some consequences for the distribution of zeros due to time-reversal symmetry are also discussed.