Edge switching transformations of quantum graphs

M. Aizenman, H. Schanz, U. Smilansky, S. Warzel

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 Schrödinger operator is interlaced with that of the original one. By implication, under edge swap the spectra before and after the transformation, denoted by {En} n =1 and { Ẽn}n =1 correspondingly, are level-2 interlaced, so that En-2 ≤ Ẽ n ≤ En+2. The proofs are guided by considerations of the quantum graphs' discrete analogs.

Original languageEnglish (US)
Pages (from-to)1699-1703
Number of pages5
JournalActa Physica Polonica A
Issue number6
StatePublished - Dec 2017

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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