A note on the integrability of non-Hermitian extensions of Calogero-Moser-Sutherland models

Abstract

We consider non-Hermitian but PT-symmetric extensions of Calogero models, which have been proposed by Basu-Mallick and Kundu for two types of Lie algebras. We address the question of whether these extensions are meaningful for all remaining Lie algebras (Coxeter groups) and if in addition one may extend the models beyond the rational case to trigonometric, hyperbolic and elliptic models. We find that all these new models remain integrable, albeit for the non-rational potentials one requires additional terms in the extension in order to compensate for the breaking of integrability.

10 pages, Latex

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• Nonlinear supersymmetry in the quantum Calogero model
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• PT-symmetric deformations of Calogero models
• Antilinear deformations of Coxeter groups, an application to Calogero models
• Spectral singularity and non-Hermitian PT-symmetric extension of $A_{N-1}$ type Calogero model without confining potential
• From real fields to complex Calogero particles
• PT-symmetric extensions of the supersymmetric Korteweg-de Vries equation
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• Complex BPS solitons with real energies from duality
• Integrable models from PT-symmetric deformations
• Constructing Exactly Solvable Pseudo-hermitian Many-particle Quantum Systems by Isospectral Deformation
• Jordan blocks and the Bethe ansatz I: The eclectic spin chain as a limit
• Deconstructing non-Dirac-hermitian supersymmetric quantum systems
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• PT-symmetrically deformed shock waves
• Particles versus fields in PT-symmetrically deformed integrable systems
• New solutions to the $s{\ell }_q(2)$-invariant Yang-Baxter equations at roots of unity
• Non-Hermitian superintegrable systems