  In this paper, we present a U(1)-invariant expansion theory of the adiabatic
process. As its application, we propose and discuss new sufficient adiabatic
approximation conditions. In the new conditions, we find a new invariant
quantity referred as quantum geometric potential (QGP) contained in all
time-dependent processes. Furthermore, we also give detailed discussion and
analysis on the properties and effects of QGP.

Quantum Physics