We explore some interesting phenomena in a simple non-Hermitian ladder system. Special modes with energy eigenvalues closely related to the inter-chain-coupling strength appear in the non-Hermitian ladder system. We show that a phase transition occurs whereby special modes with pure real eigenvalues can switch to special modes with pure imaginary eigenvalues, when the inter-chain-coupling strength changes from symmetric to asymmetric. We find that the density profiles of all the special modes are completely identical under certain conditions, even if the inter-chain-coupling strength is added into the non-Hermitian ladder system in different ways. Moreover, we also demonstrate that the different inter-chain couplings are fundamentally equivalent to adding different on-site potential energies into the non-Hermitian ladder system.

中文翻译：

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非Hermitian阶梯系统中链间耦合引起的特殊模式

我们在简单的非Hermitian阶梯系统中探索一些有趣的现象。能量特征值与链间耦合强度密切相关的特殊模式出现在非埃尔米特阶梯系统中。我们表明，当链间耦合强度从对称变为不对称时，会发生相变，从而使具有纯真实特征值的特殊模式切换为具有纯虚特性值的特殊模式。我们发现，即使将链间耦合强度以不同方式添加到非Hermitian阶梯系统中，所有特殊模式的密度分布在特定条件下也完全相同。此外，我们还证明了不同的链间耦合从根本上等同于向非Hermitian阶梯系统中添加不同的现场势能。