Change in the adiabatic invariant in a nonlinear two-mode model of   Feshbach resonance passage
  Mean-field approach has recently been used to model coupled atom-molecular Bose-Einstein condensates (BEC) and coupled Fermi-Bose condensates near Feshbach resonance. Sweeping of magnetic field across the resonance gives a new (nonlinear) version of Landau-Zener problem. We investigate the structure of the corresponding classical phase space and calculate change in the action which corresponds to finite-rate efficiency of the sweep. We consider the case of non-zero initial action, which corresponds to some finite initial molecular fraction. 
A.P. Itin, A.A. Vasiliev, S. Watanabe, and G.Krishna