论文标题
连接多样的网络中的本地化和定位
Localization and delocalization in networks with varied connectivity
论文作者
论文摘要
我们研究了电路QED网络中的定位和定位现象，其连通性从有限范围到全耦合都不同。我们发现相互作用与连通性之间有一个引人入胜的相互作用。特别是（i）谐波（ii）Jaynes-Cummings和（iii）Bose-Hubbard网络。我们从填充网络中的一个节点的初始条件开始，然后及时演变。时间动力学和稳态表征了这些大型网络中本地化（自我捕获）的特征。对于谐波网络的情况，获得了精确的分析结果，我们证明了全部连接显示自捕获，而有限型连接性的连接显示了DELECALIAD。相互作用的情况（Jaynes-Cummings，Bose-Hubbard网络）通过精确的量子动力学和半古典方法研究了。当一个人的连通性范围和相互作用的强度变化时，我们会获得一个有趣的相图。我们研究了腔/量子的不完美的后果以及不可避免的疾病的作用。我们的结果是相关的，尤其是考虑到具有远程连接性的工程系统的最新实验进展。
We study the phenomenon of localization and delocalization in a circuit-QED network with connectivity varying from finite-range to all-to-all coupling. We find a fascinating interplay between interactions and connectivity. In particular, we consider (i) Harmonic (ii) Jaynes-Cummings and (iii) Bose-Hubbard networks. We start with the initial condition where one of the nodes in the network is populated and then let it evolve in time. The time dynamics and steady state characterize the features of localization (self-trapping) in these large-scale networks. For the case of Harmonic networks, exact analytical results are obtained and we demonstrate that all-to-all connection shows self-trapping whereas the finite-ranged connectivity shows delocalization. The interacting cases (Jaynes-Cummings, Bose-Hubbard networks) are investigated both via exact quantum dynamics and semi-classical approach. We obtain an interesting phase diagram when one varies the range of connectivity and the strength of the interaction. We investigate the consequence of imperfections in the cavity/qubit and the role of inevitable disorder. Our results are relevant especially given recent experimental progress in engineering systems with long-range connectivity.
