dc.contributor.author | Maltsev, A | |
dc.date.accessioned | 2024-04-26T08:47:35Z | |
dc.date.available | 2024-03-25 | |
dc.date.available | 2024-04-26T08:47:35Z | |
dc.date.issued | 2024 | |
dc.identifier.issn | 1664-0403 | |
dc.identifier.uri | https://qmro.qmul.ac.uk/xmlui/handle/123456789/96453 | |
dc.description.abstract | Quantum graphs without interaction which contain equilateral cycles possess “topological” bound states which do not correspond to zeros of one of the two variants of the secular equation for quantum graphs. Instead, their eigenvalues lie in the set of singularities of the vertex-scattering secular matrix. This observation turns out to be representative of a wider phenomenon. We introduce a notion of topological bound states and show that they are linear combinations of functions supported on generators of the fundamental group of the graph (hence the “topological” in the name), including for graphs that have interactions on the edges. Using an Ihara-style theorem, we elucidate the role of such topological bound states in the spectral analysis of quantum graph Hamiltonians using secular matrices. En route we determine the set of the fixed vectors of the bond-scattering matrix. | |
dc.publisher | EMS Press | en_US |
dc.relation.ispartof | Journal of Spectral Theory | |
dc.rights | This item is distributed under the terms of the Creative Commons Attribution 4.0 Unported License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. | |
dc.subject | quantum graph | en_US |
dc.title | On topological bound states and secular equations for quantum-graph eigenvalues | en_US |
dc.type | Article | en_US |
dc.rights.holder | © 2024 the Author(s). Published by EMS Press | |
pubs.notes | Not known | en_US |
pubs.publication-status | Accepted | en_US |
dcterms.dateAccepted | 2024-03-25 | |
rioxxterms.funder | Default funder | en_US |
rioxxterms.identifier.project | Default project | en_US |
qmul.funder | Spectral Universality for Random Matrices::Royal Society | en_US |