Quick search Find article
Quick search
Find article

{\cal PT} -symmetric deformations of Calogero models

Andreas Fring1 and Miloslav Znojil2

Show affiliations


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



  1. {\cal PT} -symmetric deformations of Calogero models

    Andreas Fring and Miloslav Znojil 2008 J. Phys. A: Math. Theor. 41 194010

  2. A general framework for recursive decompositions of unitary quantum evolutions

    Mehmet Dağlı et al 2008 J. Phys. A: Math. Theor. 41 155302

  3. DNA-wrapped carbon nanotubes

    A N Enyashin et al 2007 Nanotechnology 18 245702

  4. Evaluation of new spin foam vertex amplitudes

    Igor Khavkine 2009 Class. Quantum Grav. 26 125012

  5. Target detection in shallow-water reverberation based on parameter-induced stochastic resonance

    Huiquan Zhang et al 2008 J. Phys. A: Math. Theor. 41 105003

  6. Modelling of the OCS/SODART Observations of SN Remnants

    A Finoguenov et al 1998 Phys. Scr. 1998 139

  7. Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry

    C Quesne 2008 J. Phys. A: Math. Theor. 41 392001

  8. The missing angular momentum of superconductors

    J E Hirsch 2008 J. Phys.: Condens. Matter 20 235233

  9. Derivation of the relativistic 'proper-time' quantum evolution equations from canonical invariance

    Moshe Shapiro 2008 J. Phys. A: Math. Theor. 41 175303

  10. Non-linear susceptibility studies of La0.85Ca0.15Mn0.95Fe0.05O3

    Hadayat Ullah Khan et al 2007 J. Phys.: Condens. Matter 19 106202

View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.