Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions
| Autor: | Berkolaiko, G., Weyand, T. |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Phil. Trans. Roy. Soc. A. 372, 1471-2962 (2014) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1098/rsta.2012.0522 |
| Popis: | We prove an analogue of the magnetic nodal theorem on quantum graphs: the number of zeros $\phi$ of the $n$-th eigenfunction of the Schr\"odinger operator on a quantum graph is related to the stability of the $n$-th eigenvalue of the perturbation of the operator by magnetic potential. More precisely, we consider the $n$-th eigenvalue as a function of the magnetic perturbation and show that its Morse index at zero magnetic field is equal to $\phi - (n-1)$. Comment: 19 pages, 3 figures |
| Databáze: | arXiv |
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