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 nonzero initial action, which corresponds to some finite initial molecular fraction.