PL EN


Preferences help
enabled [disable] Abstract
Number of results
2017 | 132 | 6 | 1699-1703
Article title

Edge Switching Transformations of Quantum Graphs

Content
Title variants
Languages of publication
EN
Abstracts
EN
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 ≤ Ẽₙ ≤ Eₙ₊₂. The proofs are guided by considerations of the quantum graphs' discrete analogs.
Keywords
EN
Publisher

Year
Volume
132
Issue
6
Pages
1699-1703
Physical description
Dates
published
2017-12
Contributors
author
  • Departments of Physics and Mathematics, Princeton University, Princeton NJ 08540, USA
author
  • Institute of Mechanical Engineering, University of Applied Sciences Magdeburg-Stendal, D-39114 Magdeburg, Germany
author
  • Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
author
  • Zentrum Mathematik, TU München, Boltzmannstr. 3, 85747 Garching, Germany
References
  • [1] L. Pauling, J. Chem. Phys. 4, 673 (1936), doi: 10.1063/1.1749766
  • [2] T. Kottos, U. Smilansky, Phys. Rev. Lett. 79, 4794 (1997), doi: 10.1103/PhysRevLett.79.4794
  • [3] T. Kottos, U. Smilansky, Ann. Phys. 274, 76 (1999), doi: 10.1006/aphy.1999.5904
  • [4] S. Gnutzmann, Uzy Smilansky, Adv. Phys. 55, 527 (2006), doi: 10.1080/00018730600908042
  • [5] P. Kuchment, Analysis on Graphs, its Applications, Proc. Symp. Pure. Math. 77, AMS 2008, p. 291, doi: 10.1090/pspum/077
  • [6] G. Berkolaiko, P. Kuchment, Introduction to Quantum Graphs, AMS Mathematical Surveys and Monographs, vol. 186, 2012, doi: 10.1090/surv/186
  • [7] O. Post, Spectral analysis on graph-like spaces, Lecture Notes in Mathematics 2039, Springer 2012, doi: 10.1007/978-3-642-23840-6
  • [8] J.J. Seidel, in: Proc. Fifth Southeastern Conference on Combinatorics, Graph Theory, Computing Congressus Numerantium X, Utilitas Math, Winnipeg, MB (1974), p.125 http://catalog.hathitrust.org/Record/000500884
  • [9] B. Gutkin, U. Smilansky, J. Phys A. 31, 6061 (2001), doi: 10.1088/0305-4470/34/31/301
  • [10] M. Kac, Am. Math. Month. 73, 1 (1966), doi: 10.2307/2313748
  • [11] B. Simon, in: CRM Proceedings and Lecture Notes, Vol. 8, 1995, p. 109
  • [12] S. Albeverio, K. Pankrashkin, J. Phys A 38, 4859 (2005), doi: 10.1088/0305-4470/38/22/010
  • [13] J. Behrndt, M.M. Malamud, H. Neidhardt, Proc. Lond. Math. Soc. 97, 568 (2008), doi: 10.1112/plms/pdn016
  • [14] H. Weyl, Math. Ann. 71, 441 (1912), doi: 10.1007/BF01456804
  • [15] D. Hundertmark, E.H. Lieb, L.E. Thomas, Adv. Theor. Math. Phys. 2, 719 (1998), doi: 10.4310/ATMP.1998.v2.n4.a2
  • [16] F.J. Dyson, J. Math. Phys. 3, 140 (1962), doi: 10.1063/1.1703773
  • [16a] F.J. Dyson, J. Math. Phys. 3, 157 (1962), doi: 10.1063/1.170377
  • [16] F.J. Dyson, J. Math. Phys. 3, 166 (1962), doi: 10.1063/1.170377
  • [17] C.H. Joyner, U. Smilansky, J. Phys. A: Math. Theor. 48 (2015), doi: 10.1088/1751-8113/48/25/255101
  • [18] R. Band, G. Berkolaiko, H. Raz, U. Smilansky, Comm. Math. Phys. 311, 815 (2012), doi: 10.1007/s00220-011-1384-9
  • [19] O. Hul, S. Bauch, P. Pakoński, N. Savytskyy, K. Zyczkowski, L. Sirko, Phys. Rev. E 69, 056205 (2004), doi: 10.1103/PhysRevE.69.056205
  • [20] P. Kurasov, G. Malenová, S. Naboko, J. Phys. A 46, 275309 (2013), doi: 10.1088/1751-8113/46/27/275309
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv132n6p09kz
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.