On the Nodal Count Statistics for Separable Systems in any Dimension

TL;DR

This paper investigates the statistical distribution of nodal domains for eigenfunctions of separable wave equations in any dimension, providing explicit formulas and analyzing universal properties through examples and numerical data.

Contribution

It introduces an explicit expression for the limiting distribution of normalized nodal counts in separable systems across arbitrary dimensions.

Findings

Derived explicit limiting distribution formula

Identified universal properties of nodal count statistics

Validated results with examples and numerical analysis

Abstract

We consider the statistics of the number of nodal domains aka nodal counts for eigenfunctions of separable wave equations in arbitrary dimension. We give an explicit expression for the limiting distribution of normalised nodal counts and analyse some of its universal properties. Our results are illustrated by detailed discussion of simple examples and numerical nodal count distributions.