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## Non-Hermitian oscillators with $$T_d$$ symmetry

Paolo Amore, Francisco M. Fernández, Javier Garcia

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 $$g$$.

http://arxiv.org/abs/1409.2672
Quantum Physics (quant-ph)