Degeneracies in the length spectra of metric graphs
| Autor: | Gavish, U., Smilansky, U. |
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| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | J. Phys. A: Math. Theor. 40 (2007) 10009-10020 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1751-8113/40/33/006 |
| Popis: | The spectral theory of quantum graphs is related via an exact trace formula with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The latter is a degenerate spectrum, and understanding its structure (i.e.,finding out how many different lengths exist for periodic orbits with a given period and the average number of periodic orbits with the same length) is necessary for the systematic study of spectral fluctuations using the trace formula. This is a combinatorial problem which we solve exactly for complete (fully connected) graphs with arbitrary number of vertices. Comment: 13 pages, 7 figures |
| Databáze: | arXiv |
| Externí odkaz: |
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