A bifurcation phenomenon of Stokes curves around a double turning point, and influence of virtual turning points upon the transition probabilities for three-level systems

We study the non-adiabatic transition problem of three-level systems from the viewpoint of the exact WKB analysis. We show the importance of virtual turning points and new Stokes curves in this problem by presenting some concrete examples where the contribution of virtual turning points to transition probabilities becomes greater than that of ordinary turning points. In the course of our discussion we encounter a bifurcation phenomenon of Stokes curves around a double turning point, and we investigate this issue as well.