  The dynamics of quantum systems under the adiabatic Hamiltonian has attracted
attention not only in quantum control but also in a wide range of fields from
condensed matter physics to high-energy physics because of its non-perturbative
behavior. Here we analyze the adiabatic dynamics in the two-level systems and
the multilevel systems using the exact WKB analysis, which is one of the
non-perturbative analysis methods. As a result, we obtain a formula for the
transition probability, which is similar to the known formula in the two-level
system. Although non-perturbative analysis in the adiabatic limit has rarely
been studied for multilevel systems, we show that the same analysis can be
applied and also provide a concrete example. The results will serve as a basis
for the application of the exact WKB analysis in various fields of physics.
