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Edge Switching Transformations of Quantum Graphs

Author(s): Aizenman, Michael; Schanz, H; Smilansky, U; Warzel, S

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Abstract: 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 Schrodinger 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)(infinity) and (E) over bar (n)(n=1)(infinity) correspondingly, are level-2 interlaced, so that En-2 <= (E) over bar (n) <= En+2. The proofs are guided by considerations of the quantum graphs’ discrete analogs.
Publication Date: Dec-2017
Citation: Aizenman, M, Schanz, H, Smilansky, U, Warzel, S. (2017). Edge Switching Transformations of Quantum Graphs. ACTA PHYSICA POLONICA A, 132 (1699 - 1703. doi:10.12693/APhysPolA.132.1699
DOI: doi:10.12693/APhysPolA.132.1699
ISSN: 0587-4246
EISSN: 1898-794X
Pages: 1699 - 1703
Type of Material: Journal Article
Journal/Proceeding Title: ACTA PHYSICA POLONICA A
Version: Author's manuscript

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