Statistics of Wave Functions in Coupled Chaotic Systems

TL;DR

This paper uses supersymmetry to derive the joint distribution of wavefunction densities in coupled chaotic systems, revealing universal spatial correlations and eigenstate hybridization effects.

Contribution

It provides the first exact calculation of wavefunction correlations in coupled chaotic systems, highlighting universality and novel spatial correlations.

Findings

Discovered universal spatial correlations in coupled systems

Derived exact joint distribution of wavefunction densities

Showed eigenstate hybridization in weak coupling regime

Abstract

Using the supersymmetry technique, we calculate the joint distribution of local densities of electron wavefunctions in two coupled disordered or chaotic quantum billiards. We find novel spatial correlations that are absent in a single chaotic system. Our exact result can be interpreted for small coupling in terms of the hybridization of eigenstates of the isolated billiards. We show that the presented picture is universal, independent of microscopic details of the coupling.