  Cosmological particle production by a time-dependent scalar field is common
in cosmology. We focus on the mechanism of asymmetry production when
interaction explicitly violates symmetry and its motion is rapid enough to
create particles by itself. Combining the exact WKB analysis and the
Landau-Zener transition, we point out that perturbation before the
non-perturbative analysis may drastically change the structure of the Stokes
lines of the theory. The Exact WKB can play an important role in avoiding such
discrepancies.
