This article aims to study the existence of stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian system when exposed to external fields. We investigate a non-Hermitian $\mathcal{PT}$-symmetric diamond chain network and its transport dynamics in two different situations, namely in a flat-band case and a non-flat-band case. The considered system does not support an unbroken-$\mathcal{PT}$ phase or completely real eigenspectra in any of the parametric regions in both the flat- and non-flat-band cases. In the flat-band case, up to a critical value of the gain-loss parameter, the bands are found to be gapless or inseparable, and for other values the bands are isolated. Considering the non-flat-band case, all the bands are found to be complex dispersive and are also isolated. In the case of a completely broken $\mathcal{PT}$ phase, we look at the possibility of having stable dynamics or Bloch oscillations upon the application of external fields like a synthetic electric field. In particular, when the complex bands are isolated, we point out that the Landau-Zener tunneling induced by the synthetic electric field can enable Bloch oscillations. The amplitude of these Bloch oscillations is large and persists for a long propagation distance, which reveals that super Bloch oscillations can be observed in the broken $\mathcal{PT}$ phase of the system. We also report the amplified Bloch oscillations, which pave the way toward controlling transport phenomena in non-Hermitian systems.

中文翻译：

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非HermitianPT对称平带晶格中的稳定Bloch振荡和Landau-Zener隧穿

本文旨在研究非Hermitian系统中暴露于外部电场时稳定Bloch振荡和Landau-Zener隧道的存在。我们调查非赫米特语$\mathcal{PT}$对称金刚石链网络及其在两种不同情况下的传输动力学，即在平带情况下和非平带情况下。考虑的系统不支持不间断的-$\mathcal{PT}$平带和非平带情况下任何参数区域中的相位或完全实特征谱。在平坦频带的情况下，直到增益损耗参数的临界值，频带都是无间隙的或不可分割的，而对于其他值，频带是隔离的。考虑到非平坦频带的情况，发现所有频带都是复杂的色散并且也被隔离。在完全破裂的情况下$\mathcal{PT}$阶段，我们研究在施加诸如合成电场之类的外部电场时具有稳定动力学或Bloch振荡的可能性。特别是，当隔离复杂的谱带时，我们指出由合成电场引起的Landau-Zener隧穿能够实现布洛赫振荡。这些Bloch振荡的振幅很大，并且持续了很长的传播距离，这表明可以在断裂中观察到超Bloch振荡。$\mathcal{PT}$系统阶段。我们还报告了放大的布洛赫振荡，这为控制非埃尔米特系统中的传输现象铺平了道路。