论文标题
在量子图中扩散的障碍：基于几何的上限在光谱间隙上
Impediments to diffusion in quantum graphs: geometry-based upper bounds on the spectral gap
论文作者
论文摘要
我们在紧凑型公制图上具有标准或dirichlet顶点条件的Laplacian的光谱间隙上的几个上限。特别是，我们根据最短循环（周长），直径，图的总长度以及此处首次引入的进一步的度量量（例如回避直径）获得估计值。使用有关Ramanujan图，一类扩展器图的已知结果，我们还证明了其中一些度量量或组合的一些结果不会以正确的缩放范围传递任何光谱界。
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.
