CO2 molecule as a quantum realization of the 1:1:2 resonant swing-spring with monodromy.
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.
Mathematisch Instituut, Universiteit Utrecht, 3508 TA Utrecht, The Netherlands.
R H
RH
Cushman
H R
HR
Dullin
A
A
Giacobbe
D D
DD
Holm
M
M
Joyeux
P
P
Lynch
D A
DA
Sadovskií
B I
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Zhilinskií