量子图中扩散的障碍：基于几何的谱隙上界
Impediments to diffusion in quantum graphs: geometry-based upper bounds on the spectral gap
AI总结：
本文在紧致度量图上研究Laplacian谱隙的几何上界，引入回避直径等新度量量，并利用Ramanujan图证明部分度量量无法提供正确标度的谱界。
摘要：
我们针对紧致度量图上具有标准或Dirichlet顶点条件的Laplacian算子，推导了谱隙的若干上界。特别地，我们得到了基于最短环长度（围长）、直径、图的总长度以及本文首次引入的进一步度量量（如回避直径）的估计。利用关于Ramanujan图（一类扩展图）的已知结果，我们还证明了其中一些度量量或其组合无法给出具有正确标度的谱界。
英文摘要：
We derive several upper bounds on the spectral gap of the Laplacian with standard or Dirichlet vertex conditions on compact metric graphs. In particular, we obtain estimates based on the length of a shortest cycle (girth), diameter, total length of the graph, as well as further metric quantities introduced here for the first time, such as the avoidance diameter. Using known results about Ramanujan graphs, a class of expander graphs, we also prove that some of these metric quantities, or combinations thereof, do not to deliver any spectral bounds with the correct scaling.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
