Supersymmetry, PT-symmetry and spectral bifurcation

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 su...

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Bibliographic Details
Published in:Annals of physics 2010-06, Vol.325 (6), p.1198-1206
Main Authors: Abhinav, Kumar, Panigrahi, P.K.
Format: Article
Language:English
Subjects:
BANACH SPACE
BIFURCATION
Bifurcations
C INVARIANCE
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
ENERGY SPECTRA
HILBERT SPACE
Invariance
INVARIANCE PRINCIPLES
MATHEMATICAL SPACE
P INVARIANCE
Particle physics
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Platinum
POTENTIALS
PT-symmetry
Quantum physics
SPACE
SPECTRA
SUPERSYMMETRY
SYMMETRY
T INVARIANCE
Two phase
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Summary: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 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 complex parametric shifts.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2010.04.003