We first review the localization-delocalization transition of a non-Hermitian random tight-binding Anderson model, called the Hatano-Nelson model. We then report a new result for a non-Hermitian extension of a discrete-time quantum walk on a one-dimensional random medium; we numerically find a delocalization transition similar to one of the Hatano-Nelson model. As a common feature to both models, at the transition point, an eigenvector gets delocalized and at the same time the corresponding energy eigenvalue (for the latter quantum-walk model, the imaginary unit times the phase of the eigenvalue of the time-evolution operator) becomes complex. One of the unique properties of the present non-Hermitian quantum walk is that the localization length of all eigenvectors is the same, and thereby all eigenstates simultaneously undergo the delocalization transition and all eigenvalues become complex at the same time when we turn up a non-Hermitian parameter.

我们首先回顾了非 Hermitian 随机紧束缚 Anderson 模型（称为 Hatano-Nelson 模型）的定位-离域转换。然后，我们报告了一维随机介质上离散时间量子游走的非厄米扩展的新结果；我们在数值上找到了类似于 Hatano-Nelson 模型之一的离域转换。作为这两种模型的共同特征，在过渡点，特征向量被离域，同时相应的能量特征值（对于后一种量子行走模型，虚数单位乘以时间演化算子的​​特征值的相位) 变得复杂。当前非厄米量子游走的独特性质之一是所有特征向量的局部化长度相同，