Non-Hermitian oscillators with $T_d$ symmetry

Abstract

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 $g$.

References in corpus (2)

• Is space-time symmetry a suitable generalization of parity-time symmetry?
• PT phase transition in multidimensional quantum systems

Cited by in corpus (2)

• Spectrum and normal modes of non-hermitian quadratic boson operators
• On the symmetry of three identical interacting particles in a one-dimensional box