  An innovative microscopic model with a minimal number of parameters:
tunneling splitting gap, external field sweeping velocity, and decoherence rate
is used to describe dynamics of the dissipative Landau-Zener transition in the
presence of the decoherence. In limiting cases, the derived equation of motion
gives rise to the well-known Landau-Zener and Kayanuma formula. In a general
case, the description demonstrates a non-monotonic flipping probability with
respect to the sweeping velocity, which is also found in some other models.
This non-monotony can be explained by considering the competition and timescale
of the quantum tunneling, crossing period, and decoherence process. The
simplicity and robustness of the theory offer a practical and novel description
of the Landau-Zener transition. In addition, it promises an alternative method
to the electron paramagnetic resonance in measuring the effective decoherence
rate of relevant quantum systems.
