Exact WKB Analysis of Non-adiabatic Transition Problems for 3-Levels

Abstract

As we have observed so far, virtual turning points and (new) Stokes curves emanating from them play a crucially important role in discussing the Stokes geometry of a higher order ordinary differential equation and/or a system of ordinary differential equations of size greater than two. Once all the non-redundant virtual turning points are provided, then we can explicitly calculate the analytic continuation of solutions of an ordinary differential equation in view of its complete Stokes geometry and connection formulas discussed in Sect. 1.4. Adopting this approach, we consider the non-adiabatic transition problem for three levels and compute transition probabilities of solutions in this chapter. This is a good application of the exact WKB analysis for a higher order ordinary differential equation to a physical problem, illuminating the role of virtual turning points in the calculation of analytic continuation of solutions.