The Exact WKB analysis for asymmetric scalar preheating
  Using the exact WKB analysis of the higher-order differential equation, we
analyze the mechanism of asymmetric preheating of a complex scalar field. The
solution requires the Stokes phenomena of the fourth-order differential
equation. We have identified the Stokes phenomena, which are crucial for the
matter-antimatter asymmetry. The new Stokes lines and the virtual turning
points, which are developed to analyze the Stokes phenomena of the higher-order
differential equations, are crucial for global consistency but do not introduce
a new effect in this model.
