论文标题
比较Schrödinger操作员在量子图上的频谱
Comparing the spectrum of Schrödinger operators on quantum graphs
论文作者
论文摘要
我们在紧凑型有限度量图上研究Schrödinger操作员，但符合$δ$耦合和标准边界条件。我们比较了这些自我接合实现的特征值的$ n $ th，并获得了偏差平均值的渐近结果。通过这样做，我们概括了Rudnick等人的最新结果。 $ \ mathbb {r}^2 $在量子图设置中获得的域获得。这也导致了以前的相关结果的概括，并在[arxiv：2212.09143]和[arxiv：2212.12531]中独立获得了公制图。此外，基于我们的主要结果，我们引入了一些（量子）图的圆周概念，这些概念可能在将来被证明是有用的。
We study Schrödinger operators on compact finite metric graphs subject to $δ$-coupling and standard boundary conditions. We compare the $n$-th eigenvalues of those self-adjoint realizations and derive an asymptotic result for the mean value of deviations. By doing this, we generalize recent results from Rudnick et al. obtained for domains in $\mathbb{R}^2$ to the setting of quantum graphs. This also leads to a generalization of related results previously and independently obtained in [arXiv:2212.09143] and [arXiv:2212.12531] for metric graphs. In addition, based on our main result, we introduce some notions of circumference for a (quantum) graph which might prove useful in the future.
