  We present a general theory for adiabatic evolution of quantum states as
governed by the nonlinear Schrodinger equation, and provide examples of
applications with a nonlinear tunneling model for Bose-Einstein condensates.
Our theory not only spells out conditions for adiabatic evolution of
eigenstates, but also characterizes the motion of non-eigenstates which cannot
be obtained from the former in the absence of the superposition principle. We
find that in the adiabatic evolution of non-eigenstates, the Aharonov-Anandan
phases play the role of classical canonical actions.
