Impediments to diffusion in quantum graphs: Geometry-based upper bounds on the spectral gap
Impediments to diffusion in quantum graphs: Geometry-based upper bounds on the spectral gap
复制标题
量子图中扩散的障碍：基于几何的光谱间隙上限
DOI：
10.1090/proc/16322
复制
发表时间：
2023
影响因子：
1
通讯作者：
Mugnolo, Delio
中科院分区：
文献类型：
--
作者：
Berkolaiko, Gregory;Kennedy, James;Kurasov, Pavel;Mugnolo, Delio
在标准或Dirichlet点条件下，我们得到了紧度量图上拉普拉斯算子谱间隙的几个上界。特别地，我们基于最短圈的长度(周长)、直径、图的总长度以及第一次引入的进一步的度量量，例如避免直径，得到估计。利用关于Ramanujan图的已知结果，我们还证明了这些度量值中的一些或它们的组合在正确的尺度下不提供任何谱界。参考文献
We derive several upper bounds on the spectral gap of the Laplacian on compact metric graphs with standard or Dirichlet vertex conditions. 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. References