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We consider the level-crossing problem in a three-level system withnon-linearly time-varying Hamiltonian (time-dependence $t^{-3}$). We study thevalidity of the so-called independent crossing approximation in theLandau-Zener model by making comparison with results obtained numerically indensity matrix approach. We also demonstrate the failure of the so-called"nearest zero" approximation of the Landau-Zener level-crossing probabilityintegral.Comment: 11 pages, 3 figures. To be published in Physical Review

Landau-Zener problem in a three-level neutrino system with nonlinear time dependence