dc.contributor.author | II, EMH | en_US |
dc.contributor.author | Maltsev, AV | en_US |
dc.date.accessioned | 2019-06-24T15:17:14Z | |
dc.date.available | 2018-03-05 | en_US |
dc.date.submitted | 2018-03-28T15:08:32.906Z | |
dc.identifier.issn | 0002-9947 | en_US |
dc.identifier.uri | https://qmro.qmul.ac.uk/xmlui/handle/123456789/58186 | |
dc.description | 6 figures | en_US |
dc.description | 6 figures | en_US |
dc.description | 6 figures | en_US |
dc.description.abstract | We 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.publisher | American Mathematical Society | en_US |
dc.relation.ispartof | Transactions of the American Mathematical Society | en_US |
dc.rights | This is a pre-copyedited, author-produced version of an article accepted for publication in On Agmon metrics following peer review. | |
dc.rights | This is a pre-copyedited, author-produced version of an article accepted for publication in Transactions of the American Mathematical Society following peer review. | |
dc.subject | math.SP | en_US |
dc.subject | math.SP | en_US |
dc.title | Localization and landscape functions on quantum graphs | en_US |
dc.type | Article | |
dc.rights.holder | © Springer-Verlag GmbH Germany, part of Springer Nature 2018 | |
dc.rights.holder | © 2019 American Mathematical Society | |
dc.identifier.doi | 10.1090/tran/7908 | en_US |
pubs.author-url | http://arxiv.org/abs/1803.01186v1 | en_US |
pubs.declined | 2018-03-28T15:08:48.505+0100 | |
pubs.notes | Not known | en_US |
pubs.publication-status | Accepted | en_US |
dcterms.dateAccepted | 2018-03-05 | en_US |
rioxxterms.funder | Default funder | en_US |
rioxxterms.identifier.project | Default project | en_US |