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arXiv · 0910.2423

Supersymmetry, PT-symmetry and Spectral Bifurcation

Kumar Abhinav·Prasanta K. Panigrahi
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Abstract

We demonstrate that large class of PT-symmetric complex potentials, which can have isospectral real partner potentials, possess two different superpotentials. In the parameter domain, where the superpotential is unique, the spectrum is real and shape-invariant, leading to translational shift in a suitable parameter by \textit{real} units. The case of two different superpotentials, leading to same potential, yields broken PT-symmetry, the energy spectra in the two phases being separated by a bifurcation. Interestingly, these two superpotentials generate the two disjoint sectors of the Hilbert space. In the broken case, shape invariance produces \textit{complex} parametric shifts.

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Kumar Abhinav, Prasanta K. Panigrahi. 2009-10-13. Supersymmetry, PT-symmetry and Spectral Bifurcation. https://doi.org/10.1016/j.aop.2010.04.003

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