Comparison of quantal and classical behavior of PT-symmetric systems at avoided crossings

The quantal eigenenergy spectrum and the classical motion of the 2D system ν(x,g)=12(ωx2x2+ωy2y2)+gxy2 where g∈[−0.01,0.01] are investigated. Like in the real Hermitian systems, when this system is non-Hermitian and PT-symmetric (g<0), two regions of quantal spectrum, which behave differently under the slowly changing perturbation parameter g, are found. It was found that the most of the higher order second differences of eigenvalues as a function of perturbation parameter correspond to avoided crossings.