Higher index focus-focus singularities in the Jaynes-Cummings-Gaudin model: Symplectic invariants and monodromy

JOURNAL OF GEOMETRY AND PHYSICS

卷:87

Article

Babelon, O.¹  Doucot, B.¹ 

[1] UPMC, Univ Paris 06, Sorbonne Univ, LPTHE,UMR 7589, F-75005 Paris, France

关键词: Symplectic geometry;    Integrable systems;    Symplectic invariants;    Monodromy;    Normal modes;    Solitons;   

DOI  :  10.1016/j.geomphys.2014.07.011

来源: Elsevier

【 摘 要 】

We study the symplectic geometry of the Jaynes-Cummings-Gaudin model with n = 2m - 1 spins. We show that there are focus focus singularities of maximal Williamson type (0, 0, m). We construct the linearized normal flows in the vicinity of such a point and show that soliton type solutions extend them globally on the critical torus. This allows us to compute the leading term in the Taylor expansion of the symplectic invariants and the monodromy associated to this singularity. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free