Non-Hermitian oscillators with T-d symmetry

作者：Amore Paolo; Fernandez Francisco M^*; Garcia Javier

来源：Annals of Physics, 2015, 353: 238-251.

DOI：10.1016/j.aop.2014.11.018

• PT-symmetry
• Space-time symmetry
• Non-Hermitian Hamiltonian
• Multidimensional systems
• Point-group symmetry

We analyse some PT-symmetric oscillators' with T-d symmetry that depend on a potential parameter g. We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of g. Pairs of eigenvalues coalesce at exceptional points g(c); their magnitude roughly decreasing with the magnitude of the eigenvalues. It is difficult to estimate whether there is a phase transition at a nonzero value of g as conjectured in earlier papers. Group theory and perturbation theory enable one to predict whether a given space-time symmetry leads to real eigenvalues for sufficiently small nonzero values of g.

• 出版日期2015-2