Edge switching transformations of quantum graphs

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

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

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 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
Volume132
Issue number6
DOIs
StatePublished - Dec 2017

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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