Hamiltonian monodromy in the spectrum and dynamics of a spin-1 Bose condensate

A spin-1 Bose condensate in a magnetic field in the single mode approximation -- valid for sufficiently small condensates -- represents a rather simple dynamical system. In this talk I will show that there is nevertheless scope for some rather unusual behavior. In particular, this system displays the phenomenon of \emph{Hamiltonian monodromy}, a topological obstruction to the existence of global action-angle variables. I will discuss the signatures of this phenomenon in the classical dynamics and quantum spectrum