  We study a classical integrable (Neumann) model describing the motion of a
particle on the sphere, subject to harmonic forces. We tackle the problem in
the infinite dimensional limit by introducing a soft version in which the
spherical constraint is imposed only on average over initial conditions. We
show that the Generalized Gibbs Ensemble captures the long-time averages of the
soft model. We reveal the full dynamic phase diagram with extended,
quasi-condensed, coordinate-, and coordinate and momentum-condensed phases. The
scaling properties of the fluctuations allow us to establish in which cases the
strict and soft spherical constraints are equivalent, confirming the validity
of the GGE hypothesis for the Neumann model on a large portion of the dynamic
phase diagram.
