Supersymmetry, PT-symmetry and Spectral Bifurcation

Details Supersymmetry, PT-symmetry and Spectral Bifurcation Supersymmetry, PT-symmetry and Spectral Bifurcation

2009-10-13

arxiv.org/abs/0910.2423v4

Annals of Physics,325:1198-1206, 2010

Physics

Quantum Physics

9 pages, 1 table

Scientific paper

10.1016/j.aop.2010.04.003

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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