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{\cal PT} -symmetric deformations of Calogero models

Andreas Fring1 and Miloslav Znojil2

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We demonstrate that Coxeter groups allow for complex {\cal PT} -symmetric deformations across the boundaries of all Weyl chambers. We compute the explicit deformations for the A2 and G2-Coxeter group and apply these constructions to Calogero–Moser–Sutherland models invariant under the extended Coxeter groups. The eigenspectra for the deformed models are real and contain the spectra of the undeformed case as subsystems.


PACS

03.65.Fd Algebraic methods

02.10.Ud Linear algebra

03.65.Ge Solutions of wave equations: bound states

02.20.Uw Quantum groups

MSC

15A18 Eigenvalues, singular values, and eigenvectors

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

81Rxx Groups and algebras in quantum theory

17B37 Quantum groups (quantized enveloping algebras) and related deformations (See also 16W35, 20G42, 81R50, 82B23)

20F55 Reflection and Coxeter groups (See also 22E40, 51F15)

Subjects

Mathematical physics

Quantum information and quantum mechanics

Dates

Issue 19 (16 May 2008)

Received 6 February 2008, in final form 10 March 2008

Published 29 April 2008



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