English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A shape invariant nonseparable and nondiagonalizable three-dimensional modelwith quadratic complex interaction was introduced by Bardavelidze, Cannata,Ioffe, and Nishnianidze. However, the complete hidden symmetry algebra and thedescription of the associated states that form Jordan blocks remained to bestudied. We present a set of six operators $\{A^{\pm},B^{\pm},C^{\pm}\}$ thatcan be combined to build a ${\mathfrak{gl}}(3)$ hidden algebra. The latter canbe embedded in an ${\mathfrak{sp}}(6)$ algebra, as well as in an${\mathfrak{osp}}(1/6)$ superalgebra. The states associated with theeigenstates and making Jordan blocks are induced in different ways bycombinations of operators acting on the ground state. We present the action ofthese operators and study the construction of an extended biorthogonal basis.These rely on establishing various nontrivial polynomial and commutatoridentities. We also make a connection between the hidden symmetry and theunderlying superintegrability property of the model. Interestingly, theintegrals generate a cubic algebra. This work demonstrates how various conceptsthat have been applied widely to Hermitian Hamiltonians, such as hiddensymmetries, superintegrability, and ladder operators, extend to thepseudo-Hermitian case with many differences.

symmetry, integrability and geometry: methods and applications

Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable  and Nondiagonalizable Modelswith Quadratic Complex Interaction. II.  Three-Dimensional Model