{"paper":{"title":"Localization and landscape functions on quantum graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Anna V. Maltsev, Evans M. Harrell II","submitted_at":"2018-03-03T15:42:35Z","abstract_excerpt":"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\n  a) responds to the potential energy $V(x)$ and to the structure of the graph in some formulaic way;\n  b) is small in examples where eigenfunctions are suppressed by the tunneling effect, and\n  c) relatively large in regions where eigenfunctions may - or may not - be concentrated, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01186","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}