Perturbative approach to time-dependent quantum systems and applications to one-crossing multistate Landau-Zener models

We formulate a perturbative approach for studying a class of multi-level time-dependent quantum systems with constant off-diagonal couplings and diabatic energies being odd functions of time. Applying this approach to a general multistate Landau-Zener (MLZ) model with all diabatic levels crossing at one point (named the one-crossing MLZ model), we derive analytical formulas of all its transition probabilities up to $4$th order in the couplings. These analytical asymptotic solutions at the diabatic limit can serve as reliable benchmarks for future studies of any unsolved one-crossing MLZ models.