Comparing the spectrum of Schr\'odinger operators on quantum graphs
| Autor: | Bifulco, Patrizio, Kerner, Joachim |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Proc. Amer. Math. Soc. (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/proc/16578 |
| Popis: | We study Schr\"odinger operators on compact finite metric graphs subject to $\delta$-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. Comment: 10 pages |
| Databáze: | arXiv |
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