Level Crossings in Complex Two-Dimensional Potentials

TL;DR

This paper investigates PT-symmetric 2D quantum systems with complex potentials, analyzing their energy spectra and the conditions under which complex eigenvalues emerge during level crossings.

Contribution

It introduces numerical and perturbative analysis of specific complex 2D potentials, revealing the relationship between PT symmetry, level crossings, and complex eigenvalues.

Findings

Complex eigenvalues occur during level crossings of same parity states.

Numerical and perturbative methods successfully compute high-level energy spectra.

PT symmetry is maintained despite the emergence of complex energies at crossings.

Abstract

Two-dimensional PT-symmetric quantum-mechanical systems with the complex cubic potential V_{12}=x^2+y^2+igxy^2 and the complex Henon-Heiles potential V_{HH}=x^2+y^2+ig(xy^2-x^3/3) are investigated. Using numerical and perturbative methods, energy spectra are obtained to high levels. Although both potentials respect the PT symmetry, the complex energy eigenvalues appear when level crossing happens between same parity eigenstates.