Level Crossings in Complex Two-Dimensional Potentials

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.

9 pages, 4 figures. Submitted as a conference proceeding of PHHQP 8

References in corpus (3)

• Making Sense of Non-Hermitian Hamiltonians
• Quantum Complex Henon-Heiles Potentials
• Interactions of Hermitian and non-Hermitian Hamiltonians

Cited by in corpus (5)

• Non-hermitean hamiltonians with unitary and antiunitary symmetry
• PT-symmetry broken by point-group symmetry
• Is space-time symmetry a suitable generalization of parity-time symmetry?
• Non-Hermitian oscillators with $T_d$ symmetry
• Mean-field approximation for a Bose-Hubbard dimer with complex interaction strength