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

Olivier Babelon, Benoit Doucot

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…