Effect of Landau－Zener tunneling by the varying sweeping rate of external field

We study the effect of Landau--Zener (LZ) tunneling caused by the varying sweeping rate of the external field, and solve the problem about the LZ tunneling rate among many levels. The LZ tunneling rate is essentially changed by the unsteady variation of the time-dependent sweeping field and is different from the steadily varying sweeping field, which makes the particles in lower states transit periodically to upper states within a finite time.