Indicators of wavefunction (de)localisation for avoided crossing in a quadrupole quantum billiard

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