Higher index focus-focus singularities in the Jayne-Cummings-Gaudin model : symplectic invariants and monodromy.

Olivier Babelon (1) , Benoît Douçot (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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.

Mots clés: symplectic geometry; symplectic invariants; monodromy; Gaudin models; solitons

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Olivier Babelon, Benoît Douçot. Higher index focus-focus singularities in the Jayne-Cummings-Gaudin model : symplectic invariants and monodromy.. 2013. ⟨hal-00921222⟩