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 $g$.

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Cited by in corpus (3)

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