Edge switching transformations of quantum graphs
| Autor: | Michael Aizenman, Uzy Smilansky, Holger Schanz, Simone Warzel |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
010102 general mathematics General Physics and Astronomy FOS: Physical sciences Mathematical Physics (math-ph) 81Q35 01 natural sciences Graph Spectral line Combinatorics Mathematics - Spectral Theory Quantum graph 0103 physical sciences FOS: Mathematics 0101 mathematics 010306 general physics Spectral Theory (math.SP) Mathematical Physics Mathematics |
| Popis: | Discussed here are the effects of basics graph transformations on the spectra of associated quantum graphs. In particular it is shown that under an edge switch the spectrum of the transformed Schr\"odinger operator is interlaced with that of the original one. By implication, under edge swap the spectra before and after the transformation, denoted by $\{ E_n\}_{n=1}^{\infty}$ and $\{\widetilde E_n\}_{n=1}^{\infty}$ correspondingly, are level-2 interlaced, so that $E_{n-2}\le \widetilde E_n\le E_{n+2}$. The proofs are guided by considerations of the quantum graphs' discrete analogs. |
| Databáze: | OpenAIRE |
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