Adiabatic condition and quantum geometric potential

In this paper, we present a $\text{U}\left(1\right)$-invariant expansion theory of the adiabatic process. As its application, we propose and discuss different sufficient adiabatic approximation conditions. In these conditions, we find an interesting invariant quantity referred to as the 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.

Figure 1

(Color online) Evolution orbit (orange or light gray without color) and adiabatic orbit (blue or dark gray without color). Both orbits are the trajectories of the polarization vectors drawn on the surface of Bloch sphere.