Topological resonances in scattering on networks (graphs).
Topological resonances in scattering on networks (graphs).
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网络（图）上散射的拓扑共振。
DOI：
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发表时间：
2012
影响因子：
8.6
通讯作者：
U. Smilansky
中科院分区：
文献类型：
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作者：
S. Gnutzmann;H. Schanz;U. Smilansky
我们报告一个迄今未被注意的类型的共振发生在散射网络（量子图），这是由于复杂的连接图的拓扑结构。我们认为通用的开放图，并表明，任何周期导致窄共振，不适合在任何突出的范例窄共振（经典障碍，本地化由于无序，混乱的散射）。我们称这些共振为“拓扑”，以强调它们的起源在非平凡的连接。拓扑共振具有清晰且唯一的签名，其在共振参数的统计中是明显的（例如，图中的宽度、延迟时间或波函数强度）。我们讨论了这种现象，通过提供数值模拟支持的分析参数，并确定上述分布的功能，这取决于真正的拓扑量，如最短的周期（周长）的长度。这些特征不能用任何其他窄共振的范例来解释。最后，我们提出了一个实验设置的拓扑共振可以证明，并研究了相关的分布函数的稳定性适度耗散。
We report on a hitherto unnoticed type of resonances occurring in scattering from networks (quantum graphs) which are due to the complex connectivity of the graph-its topology. We consider generic open graphs and show that any cycle leads to narrow resonances which do not fit in any of the prominent paradigms for narrow resonances (classical barriers, localization due to disorder, chaotic scattering). We call these resonances "topological" to emphasize their origin in the nontrivial connectivity. Topological resonances have a clear and unique signature which is apparent in the statistics of the resonance parameters (such as, e.g., the width, the delay time, or the wave-function intensity in the graph). We discuss this phenomenon by providing analytical arguments supported by numerical simulation, and identify the features of the above distributions which depend on genuine topological quantities such as the length of the shortest cycle (girth). These signatures cannot be explained using any of the other paradigms for narrow resonances. Finally, we propose an experimental setting where the topological resonances could be demonstrated, and study the stability of the relevant distribution functions to moderate dissipation.