Long-range correlations in the wave functions of chaotic systems

TL;DR

This paper analytically investigates long-range correlations in wave function amplitudes of chaotic systems, revealing finite correlations during symmetry class crossover that diminish only with localization effects.

Contribution

It provides an analytical calculation of joint amplitude distributions at distant points in chaotic systems using supersymmetry, highlighting correlation behaviors across symmetry crossovers.

Findings

Correlations vanish in pure orthogonal and unitary classes.

Correlations are finite during the crossover regime.

Localization effects can reduce these correlations.

Abstract

We study correlations of the amplitudes of wave functions of a chaotic system at large distances. For this purpose, a joint distribution function of the amplitudes at two distant points in a sample is calculated analytically using the supersymmetry technique. The result shows that, although in the limit of the orthogonal and unitary symmetry classes the correlations vanish, they are finite through the entire crossover regime and may be reduced only by localization effects.