Adiabatic Condition and Quantum Geometric Potential
  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. 
Jianda Wu, Meisheng Zhao, Jianlan Chen and Yongde Zhang