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.
Cushman
R H
RH
Mathematisch Instituut, Universiteit Utrecht, 3508 TA Utrecht, The Netherlands.
Dullin
H R
HR
Giacobbe
A
A
Holm
D D
DD
Joyeux
M
M
Lynch
P
P
Sadovskií
D A
DA
Zhilinskií
B I
BI