We discuss solvable multistate Landau–Zener (MLZ) models whose Hamiltonians have commuting partner operators with ∼1/ τ -time-dependent parameters. Many already known solvable MLZ models belong precisely to this class. We derive the integrability conditions on the parameters of such commuting operators, and demonstrate how to use such conditions in order to derive new solvable cases. We show that MLZ models from this class must contain bands of parallel diabatic energy levels. The structure of the scattering matrix and other properties are found to be the same as in the previously discussed completely solvable MLZ Hamiltonians.

中文翻译：

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具有并行能级的可积分多州Landau–Zener模型

我们讨论了可解多态Landau-Zener（MLZ）模型，其哈密顿量具有约1 /τ-时间相关参数的通勤伙伴算子。许多已知的可解MLZ模型正好属于此类。我们根据此类通勤算子的参数推导了可积性条件，并演示了如何使用此类条件来推导新的可解情形。我们表明，此类的MLZ模型必须包含平行的绝热能级带。发现散射矩阵的结构和其他特性与之前讨论的完全可解的MLZ哈密顿量相同。