标题： 开放量子系统中具有增益或损耗的电流的扩展兰道尔-布蒂克公式 显示英文标题

标题： Extended Landauer-Büttiker Formula for Current through Open Quantum Systems with Gain or Loss

摘要： 兰道尔-布蒂克公式，用于描述连接到电极的有限区域中的电流，极大地推进了我们对输运的理解。 我们利用林德布拉德-凯尔迪什形式将此公式扩展，以描述中间区域具有增益或损耗的粒子和能量电流。 基于推导出的公式，讨论了由电流中增益或损耗引起的几种新效应：增益和损耗项或系统中的反演对称性破缺可能导致电流生成；无序可以引起电流生成的异常现象；增益和损耗的存在使热导和电导连续，并确保它们即使在能带之外也遵循魏德曼-弗朗茨定律；键损耗引起的皮肤效应对电流的影响。 这项工作加深并扩展了我们对开放系统中输运现象的理解。 显示英文摘要

摘要： The Landauer-B\"{u}ttiker formula, which characterizes the current flowing through a finite region connected to leads, has significantly advanced our understanding of transport. We extend this formula to describe particle and energy currents with gain or loss in the intermediate region by using the Lindblad-Keldysh formalism. Based on the derived formula, several novel effects induced by gain or loss in the current are discussed: the breaking of inversion symmetry in the gain and loss terms or in the system can lead to current generation; the anomalous phenomenon that disorder can induce current generation; the presence of gain and loss makes the thermal and electrical conductances continuous and ensures they follow the Wiedemann-Franz law even outside the energy band; the effect of bond loss-induced skin effect on current. This work deepens and extends our understanding of transport phenomena in open systems.