Non-Hermitian Hamiltonian approach to quantum transport in disordered networks with sinks: Validity and effectiveness
Non-Hermitian Hamiltonian approach to quantum transport in disordered networks with sinks: Validity and effectiveness
复制标题
带汇的无序网络中量子传输的非厄米哈密顿方法：有效性和有效性
DOI：
10.1103/physrevb.91.094301
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发表时间：
2014
影响因子：
3.7
通讯作者：
G. Celardo
中科院分区：
文献类型：
--
作者：
G. G. Giusteri;F. Mattiotti;G. Celardo
我们研究了非厄米哈密顿方法在描述与外部环境相连的无序紧束缚网络中的量子输运时的有效性。通常，在唯象的基础上，将非厄米项添加到这样的网络中，以总结耦合到汇的影响。在这里，我们考虑一个开放的量子网络的范例模型，我们推导出一个非厄米有效模型，讨论其有效性的限制与完整的厄米模型的分析比较。具体来说，我们考虑一个环的网站连接到一个中央一维铅。引线充当吸收最初存在于环中的激发的吸收器。与电极导线的耦合强度控制环系统的打开。该模型在光捕获系统的背景下在文献中被广泛讨论。我们分析的有效性的非厄米描述在没有和存在的静态无序的环。在这两种情况下，当由环哈密顿量的本征值确定的能量范围小于铅的能带时，非厄米模型是有效的。在这种条件下，我们表明，有关的开放和无序的相互作用，以前得到的非厄米哈密顿方法，仍然有效时，充分厄米模型中存在的障碍被认为是。我们的分析结果可以扩展到通用网络与汇，导致的结论是，非厄米特的方法是有效的耦合到外部环境的能量依赖是足够光滑的能量范围内跨越的本征态的网络。
We investigate the validity of the non-Hermitian Hamiltonian approach in describing quantum transport in disordered tight-binding networks connected to external environments, acting as sinks. Usually, non-Hermitian terms are added, on a phenomenological basis, to such networks to summarize the effects of the coupling to the sinks. Here, we consider a paradigmatic model of open quantum network for which we derive a non-Hermitian effective model, discussing its limit of validity by a comparison with the analysis of the full Hermitian model. Specifically, we consider a ring of sites connected to a central one-dimensional lead. The lead acts as a sink that absorbs the excitation initially present in the ring. The coupling strength to the lead controls the opening of the ring system. This model has been widely discussed in literature in the context of light-harvesting systems. We analyze the effectiveness of the non-Hermitian description both in absence and in presence of static disorder on the ring. In both cases, the non-Hermitian model is valid when the energy range determined by the eigenvalues of the ring Hamiltonian is smaller than the energy band in the lead. Under such condition, we show that results about the interplay of opening and disorder, previously obtained within the non-Hermitian Hamiltonian approach, remain valid when the full Hermitian model in presence of disorder is considered. The results of our analysis can be extended to generic networks with sinks, leading to the conclusion that the non-Hermitian approach is valid when the energy dependence of the coupling to the external environments is sufficiently smooth in the energy range spanned by the eigenstates of the network.