Indicators of wavefunction (de)localization in the avoided crossing in a quadrupole cavity

TL;DR

This paper investigates how wavefunction localization indicators behave during avoided crossings in a quadrupole cavity, revealing that these measures, especially rms contrast, effectively identify maximal delocalization points.

Contribution

It introduces and compares three measures for wavefunction (de)localization in the context of avoided crossings, highlighting the rms contrast as the most sensitive indicator.

Findings

All measures show a minimum at the avoided crossing center.

Wavefunction is maximally delocalized at the avoided crossing.

RMS contrast is the most sensitive indicator.

Abstract

We study the relation between wavefunction (de)localization and the avoided crossing in a quadrupole billiard. We employ the inverse participation ratio, the Renyi entropy and the root-mean-square (rms) image contrast as the three types of measures for wavefunction (de)localization. It is found that all these measures behave similarly, exhibiting a minimum at the center of avoided crossing, where wavefunction is maximally delocalized. Our results show that these quantities can be good indicators for wavefunction (de)localization although the rms contrast yields the most sensitive measure among them.