Non-Hermitian (NH) systems and the Lindblad form master equation have always been regarded as reliable tools in dissipative modeling. Intriguingly, existing literature often obtains an equivalent NH Hamiltonian by neglecting the quantum jumping terms in the master equation. However, there lacks investigation into the effects of discarded terms as well as the unified connection between these two approaches. In this study, we study the Su–Schrieffer–Heeger model with collective loss and gain from a topological perspective. When the system undergoes no quantum jump events, the corresponding shape matrix exhibits the same topological properties in contrast to the traditional NH theory. Conversely, the occurrence of quantum jumps can result in a shift in the positions of the phase transition. Our study provides a qualitative analysis of the impact of quantum jumping terms and reveals their unique role in quantum systems.

中文翻译：

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拓扑扩展，包括量子跃迁

非厄米 (NH) 系统和 Lindblad 形式主方程一直被认为是耗散建模中的可靠工具。有趣的是，现有文献经常通过忽略主方程中的量子跳跃项来获得等效的 NH 哈密顿量。然而，缺乏对丢弃术语的影响以及这两种方法之间的统一联系的研究。在本研究中，我们从拓扑角度研究了具有集体损失和增益的 Su-Schrieffer-Heeger 模型。当系统没有发生量子跃迁事件时，相应的形状矩阵表现出与传统 NH 理论相同的拓扑性质。相反，量子跃迁的发生会导致相变位置的偏移。我们的研究对量子跳跃项的影响进行了定性分析，并揭示了它们在量子系统中的独特作用。