Adiabatic geometric phase of a general quantum state

A geometric phase is found for the adiabatic evolution of a general quantum state; it reduces to Berry phase when applied to eigenstates. This new phase applies to both linear quantum systems and nonlinear quantum systems, and should be particularly useful for the latter for which the adiabatic evolution of a general quantum state cannot be described in terms of a superposition of eigenstates. For linear quantum systems, our new phase becomes a statistical average of the Berry phases for all eigenstates involved.