THE CO_2 MOLECULE AS A QUANTUM REALIZATION OF THE 1:1:2 
RESONANT SWING-SPRING WITH MONODROMY

Richard H. Cushman(1), Holger R. Dullin(2), Andrea Giacobbe(1),
Darryl D. Holm(3,4), Marc Joyeux(5), Peter Lynch(6), 
Dmitrií A. Sadovskií(7), and Boris I. Zhilinskií(7)

  (1) Mathematisch Instituut, Universiteit Utrecht, 3508 TA Utrecht,
      The Netherlands
  (2) Mathematical Sciences, University of Loughborough, 
      LE113TU Loughborough, UK
  (3) Mathematics Department, Imperial College London, SW72AZ London, UK
  (4) Theoretical Division, Los Alamos National Laboratory,
      Los Alamos, NM 87545, USA
  (5) Laboratoire de Spectrométrie Physique, Université Joseph Fourier,
      UMR 5588 du CNRS, Boîte Postale 87, 38402 St. Martin d'Hčres, France
  (6) Met Éireann, Glasnevin Hill, Dublin 9, Ireland
  (7) Université du Littoral, UMR 8101 du CNRS, 
      MREID, 145 av. Maurice Schumann, 59140 Dunkerque, France 

  We consider a wide class of systems modeled by an integrable approximation
  to the three degree of freedom elastic pendulum with 1:1:2 resonance,
  or the swing-spring.  This approximation has monodromy which prohibits
  existence of global action-angle variables and complicates the dynamics.  We
  study the quantum swing-spring formed by bending and symmetric stretching
  vibrations of the CO_2 molecule. We uncover quantum monodromy of CO_2 as
  a nontrivial codimension 2 defect of the three dimensional energy--momentum
  lattice of its quantum states.

received 15 March 2004 (ms LQ9309) published 9 July 2004

Phys. Rev. Lett. 93(2) (2004) 024302.
doi: 10.1103/PhysRevLett.93.024302
URL: http://link.aps.org/abstract/PRL/v93/e024302