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arXiv · 1409.2672

Non-Hermitian oscillators with $T_{d}$ symmetry

Paolo Amore·Francisco M. Fernández·Javier Garcia
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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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Paolo Amore, Francisco M. Fernández, Javier Garcia. 2014-09-07. Non-Hermitian oscillators with $T_{d}$ symmetry. https://doi.org/10.1016/j.aop.2014.11.018

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