标题： 复杂量子网络中的记忆保持与协作屏蔽 显示英文标题

标题： Memory preservation and cooperative shielding in complex quantum networks

摘要： 复杂量子网络是建模传输现象的强大工具，特别是在生物系统中，并能够研究多体量子系统的涌现现象。高连通性和长程相互作用对系统动力学施加了强约束。在这里，我们研究由典型的XXZ哈密顿量描述的量子网络的传输特性，该网络具有非平凡的图连通性和拓扑结构以及长程相互作用。我们展示了长程相互作用如何引起保持记忆的效果，并由于协同屏蔽而强烈影响激发态的扩展。我们描述了在全连接的规则网络中距离无关耦合的记忆保持效应。确实，初始注入的激发态数量的记忆在长时间内得到保持，并编码在动力学中的频率数量中。有趣的是，我们发现记忆保持效应也出现在不太规则的图中，例如具有幂律节点连通性或复杂、小世界类型的架构的量子网络。我们讨论了这些特性在与生物学相关的问题中的意义，例如在神经科学中的韦伯定律的应用，以及通过仿生学在特定量子技术中的实现。我们还展示了长程相互作用的存在如何强烈影响小世界网络和幂律全连接网络中激发态的动力学。确实，由于协同屏蔽，随着连通性或相互作用范围的增加，初始激发态在网络中的扩散变得更慢，并且对初始条件高度依赖。 显示英文摘要

摘要： Complex quantum networks are powerful tools in the modeling of transport phenomena, particularly for biological systems, and enable the study of emergent phenomena in many-body quantum systems. High connectivity and long range interactions induce strong constraints on the system dynamics. Here, we study the transport properties of a quantum network described by the paradigmatic XXZ Hamiltonian, with non-trivial graph connectivity and topology, and long-range interaction. We show how long range interactions induce a memory preserving effects and strongly affect the spreading of the excitations due to cooperative shielding. We describe the memory-preserving effect in all-to-all connected regular networks with distance-independent couplings. Indeed the memory of the number of initially injected excitations is preserved over long times, being encoded in the number of frequencies present in the dynamics. Interestingly, we find that memory-preserving effects occur also in less regular graphs, such as quantum networks with either power-law node connectivity or complex, small-world type, architectures. We discuss the implications of these properties in biology-related problems, such as an application to Weber's law in neuroscience, and their implementation in specific quantum technologies via biomimicry. We also show how the presence of long range interaction strongly affect the dynamics of the excitations in small-world networks and power law all-to-all coupled networks. Indeed due to cooperative shielding as the connectivity or the range of interaction increase the initial excitation spreads more slowly among the network and becomes strongly dependent on the initial conditions.