Random wave functions and percolation

TL;DR

This paper supports the conjecture that nodal domains of random wave functions follow critical percolation universality, and extends it by analyzing correlation effects and level domains.

Contribution

It confirms that correlations are unimportant for universality class and distinguishes between critical and non-critical percolation for different domain types.

Findings

Nodal domains of random wave functions belong to the same universality class as critical percolation.

Wave function correlations decay slowly but are unessential for universality.

Level domains are described by non-critical percolation.

Abstract

Recently it was conjectured that nodal domains of random wave functions are adequately described by critical percolation theory. In this paper we strengthen this conjecture in two respects. First, we show that, though wave function correlations decay slowly, a careful use of Harris' criterion confirms that these correlations are unessential and nodal domains of random wave functions belong to the same universality class as non critical percolation. Second, we argue that level domains of random wave functions are described by the non-critical percolation model.