We reinvestigate the question of whether or not the dynamical symmetries of the two-dimensional interacting boson model can be transformed into each other by the quantum deformation of the algebraic structure. The deformation of both the vibrational and the rotational spectra is considered, and the breaking of the classical symmetry is measured quantitatively, while a systematic search for the best fit is performed. In no case can the quantum-deformed spectrum reach the other classical limit; only a modest improvement is observed with the phase deformation of the rotational spectrum.

03.65.Fd Algebraic methods

03.65.Vf Phases: geometric; dynamic or topological

02.10.Ud Linear algebra

02.10.De Algebraic structures and number theory

02.20.Uw Quantum groups

17B05 Structure theory

17B45 Lie algebras of linear algebraic groups (See also 14Lxx and 20Gxx)

81R40 Symmetry breaking

81R15 Operator algebra methods (See also 46Lxx, 81T05)

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

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis

Mathematical physics

Quantum information and quantum mechanics

Issue 22 (2 June 2006)

Received 30 January 2006

Published 16 May 2006