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dc.contributor.authorII, EMHen_US
dc.contributor.authorMaltsev, AVen_US
dc.date.accessioned2019-06-24T15:17:14Z
dc.date.available2018-03-05en_US
dc.date.submitted2018-03-28T15:08:32.906Z
dc.identifier.issn0002-9947en_US
dc.identifier.urihttps://qmro.qmul.ac.uk/xmlui/handle/123456789/58186
dc.description6 figuresen_US
dc.description6 figuresen_US
dc.description6 figuresen_US
dc.description.abstractWe discuss explicit landscape functions for quantum graphs. By a "landscape function" $\Upsilon(x)$ we mean a function that controls the localization properties of normalized eigenfunctions $\psi(x)$ through a pointwise inequality of the form $$ |\psi(x)| \le \Upsilon(x). $$ The ideal $\Upsilon$ is a function that a) responds to the potential energy $V(x)$ and to the structure of the graph in some formulaic way; b) is small in examples where eigenfunctions are suppressed by the tunneling effect, and c) relatively large in regions where eigenfunctions may - or may not - be concentrated, as observed in specific examples. It turns out that the connectedness of a graph can present a barrier to the existence of universal landscape functions in the high-energy r\'egime, as we show with simple examples. We therefore apply different methods in different r\'egimes determined by the values of the potential energy $V(x)$ and the eigenvalue parameter $E$.en_US
dc.publisherAmerican Mathematical Societyen_US
dc.relation.ispartofTransactions of the American Mathematical Societyen_US
dc.rightsThis is a pre-copyedited, author-produced version of an article accepted for publication in On Agmon metrics following peer review.
dc.rightsThis is a pre-copyedited, author-produced version of an article accepted for publication in Transactions of the American Mathematical Society following peer review.
dc.subjectmath.SPen_US
dc.subjectmath.SPen_US
dc.titleLocalization and landscape functions on quantum graphsen_US
dc.typeArticle
dc.rights.holder© Springer-Verlag GmbH Germany, part of Springer Nature 2018
dc.rights.holder© 2019 American Mathematical Society
dc.identifier.doi10.1090/tran/7908en_US
pubs.author-urlhttp://arxiv.org/abs/1803.01186v1en_US
pubs.declined2018-03-28T15:08:48.505+0100
pubs.notesNot knownen_US
pubs.publication-statusAccepteden_US
dcterms.dateAccepted2018-03-05en_US
rioxxterms.funderDefault funderen_US
rioxxterms.identifier.projectDefault projecten_US


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