On the Distribution of zeros of chaotic wavefunction

TL;DR

This paper investigates the statistical properties of zeros in phase-space wavefunctions of quantum chaotic systems, revealing universal short-range correlations and system-dependent long-range correlations, with implications for understanding quantum chaos.

Contribution

It provides a numerical analysis showing the existence of universal short-range and system-dependent long-range correlations among zeros in wavefunctions.

Findings

Short-range correlations are universal and independent of system parameters.

Long-range correlations depend on system specifics like symmetry and localization.

Zeros in delocalized systems mimic zeros of random functions and polynomials.

Abstract

The wavefunctions in 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 useful in the analytical calculations of the wavefunctions in quantum chaotic systems. This motivates us to persue the present study which by a numerical statistical analysis shows that both long as well as the 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 mimick that of the zeros of the random functions as well as random polynomials.