CO2 molecule as a quantum realization of the 1:1:2 resonant swing-spring with monodromy -: art. no. 024302

被引：61

作者：

Cushman, RH ^{[1
]}

Dullin, HR

Giacobbe, A

Holm, DD

Joyeux, M

Lynch, P

Sadovskií, DA

Zhilinskií, BI

机构：

[1] Univ Utrecht, Inst Math, NL-3508 TA Utrecht, Netherlands

[2] Univ Loughborough, Loughborough LE11 3TU, Leics, England

[3] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[4] Los Alamos Natl Lab, Div Theoret, Los Alamos, NM 87545 USA

[5] Univ Grenoble 1, Spectrometrie Phys Lab, F-38402 St Martin Dheres, France

[6] Met Eireann, Dublin 9, Ireland

[7] Univ Littoral, CNRS, UMR 8101, F-59140 Dunkerque, France

来源：

PHYSICAL REVIEW LETTERS | 2004年 / 93卷 / 02期

关键词：

D O I：

10.1103/PhysRevLett.93.024302

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页码：024302 / 1

页数：4

共 16 条

[1] Geometric phases, reduction and Lie-Poisson structure for the resonant three-wave interaction [J].

Alber, MS ;

Luther, GG ;

Marsden, JE ;

Robbins, JM .

PHYSICA D, 1998, 123 (1-4) :271-290

[2]

Cushman R.H., 2015, Global Aspects of Classical Integrable Systems, V2nd ed.

[3] MULTIPLE LIE-POISSON STRUCTURES, REDUCTIONS, AND GEOMETRIC PHASES FOR THE MAXWELL-BLOCH TRAVELING-WAVE EQUATIONS [J].

DAVID, D ;

HOLM, DD .

JOURNAL OF NONLINEAR SCIENCE, 1992, 2 (02) :241-262

[4] ON GLOBAL ACTION-ANGLE COORDINATES [J].

DUISTERMAAT, JJ .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1980, 33 (06) :687-706

[5] Monodromy in the resonant swing spring [J].

Dullin, H ;

Giacobbe, A ;

Cushman, R .

PHYSICA D-NONLINEAR PHENOMENA, 2004, 190 (1-2) :15-37

[6] Global bending quantum number and the absence of monodromy in the HCN⇆CNH molecule -: art. no. 032504 [J].

Efstathiou, K ;

Joyeux, M ;

Sadovskií, DA .

PHYSICAL REVIEW A, 2004, 69 (03) :032504-1

[7]

GIACOBBE A, IN PRESS

[8] Stepwise Precession of the Resonant Swinging Spring [J].

Holm, Darryl D. ;

Lynch, Peter .

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2002, 1 (01) :44-64

[9] HOMOCLINIC CHAOS IN A LASER MATTER SYSTEM [J].

HOLM, DD ;

KOVACIC, G .

PHYSICA D, 1992, 56 (2-3) :270-300

[10] Pulsation and precession of the resonant swinging spring [J].

Lynch, P ;

Houghton, C .

PHYSICA D-NONLINEAR PHENOMENA, 2004, 190 (1-2) :38-62

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