| We provide a detailed theoretical description for non-adiabatic transitions in a non-symmetric two-level Hamiltonian. Exact expressions for the Landau-Zener transition amplitudes are derived including the critical case. Our results are in very good agreement with simulations for a PT-symmetric complex crystal, showing that in many cases an effective two-mode description is appropriate. Additionally, we find the evolution matrix for the double passage scenario and discuss the possibility of conducting interferometry as multiple passages through avoided crossing regions are considered. |
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