TY - JOUR
T1 - Edge switching transformations of quantum graphs
AU - Aizenman, M.
AU - Schanz, H.
AU - Smilansky, U.
AU - Warzel, S.
N1 - Funding Information:
We thank Chris Joyner, and Rami Band for useful suggestions and corrections, and Mor Rozner for earlier numerical simulations which have guided us towards tighter results. The work of MA was supported in part by the NSF grant DMS-1613296 and the Weston Visiting Professorship at the Weizmann Institute. He thanks the Faculty of Mathematics and Computer Sciences and the Faculty of Physics at WIS for the hospitality enjoyed there.
PY - 2017/12
Y1 - 2017/12
N2 - 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.
AB - 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.
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U2 - 10.12693/APhysPolA.132.1699
DO - 10.12693/APhysPolA.132.1699
M3 - Article
AN - SCOPUS:85040074960
SN - 0587-4246
VL - 132
SP - 1699
EP - 1703
JO - Acta Physica Polonica A
JF - Acta Physica Polonica A
IS - 6
ER -