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Phys. Rev. Lett. 93, 024302 (2004) [4 pages]

CO2 Molecule as a Quantum Realization of the 1∶1∶2 Resonant Swing-Spring with Monodromy

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R. H. Cushman1, H. R. Dullin2, A. Giacobbe1, D. D. Holm3,4, M. Joyeux5, P. Lynch6, D. A. Sadovskií7, and B. I. Zhilinskií7
1Mathematisch Instituut, Universiteit Utrecht, 3508 TA Utrecht, The Netherlands
2Mathematical Sciences, University of Loughborough, Loughborough LE11 3TU, United Kingdom
3Mathematics Department, Imperial College London, London SW7 2AZ, United Kingdom
4Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
5Laboratoire de Spectrométrie Physique, Université Joseph Fourier, 38402 St. Martin d’Hères, France
6Met Éireann, Glasnevin Hill, Dublin 9, Ireland
7Université du Littoral, UMR 8101 du CNRS, 59140 Dunkerque, France

Received 15 March 2004; published 8 July 2004

We consider the wide class of systems modeled by an integrable approximation to the 3 degrees of freedom elastic pendulum with 1∶1∶2 resonance, or the swing-spring. This approximation has monodromy which prohibits the 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 CO2 molecule. We uncover quantum monodromy of CO2 as a nontrivial codimension 2 defect of the three dimensional energy-momentum lattice of its quantum states.

© 2004 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.93.024302
DOI:
10.1103/PhysRevLett.93.024302
PACS:
45.05.+x, 03.65.Sq, 33.20.Vq, 45.50.–j
 
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