# $PT$-symmetric invisible defects and confluent Darboux-Crum transformations

@article{Correa2015PTsymmetricID, title={\$PT\$-symmetric invisible defects and confluent Darboux-Crum transformations}, author={Francisco Correa and V{\'i}t Jakubsk{\'y} and Mikhail S. Plyushchay}, journal={Physical Review A}, year={2015}, volume={92}, pages={023839} }

We show that confluent Darboux-Crum transformations with emergent Jordan states are an effective tool for the design of optical systems governed by the Helmholtz equation under the paraxial approximation. The construction of generic, asymptotically real and periodic, $PT$-symmetric systems with local complex periodicity defects is discussed in detail. We show how the decay rate of the defect is related with the energy of the bound state trapped by the defect. In particular, the bound states in…

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Abstract
Hidden symmetries of non-relativistic $$ \mathfrak{so}\left(2,1\right)\cong \mathfrak{sl}\left(2,\mathrm{\mathbb{R}}\right) $$
so
2
1
≅
sl
2
ℝ
invariant systems in a cosmic…

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