{"paper":{"title":"\"Mixed spectral nature\" of Thue--Morse Hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Qinghui Liu, Xiao Yao, Yanhui Qu","submitted_at":"2015-12-25T15:40:47Z","abstract_excerpt":"We find three dense subsets $\\Sigma_I,\\Sigma_{II}$ and $\\Sigma_{III}$ of the spectrum of the Thue-Morse Hamiltonian, such that each energy in $\\Sigma_I$ is extended, each energy in $\\Sigma_{II}$ is pseudo-localized and each energy in $\\Sigma_{III}$ is one-sided pseudo-localized. We also obtain exact estimations on the norm of the transfer matrices and the norm of the formal solutions for these energies. Especially, for $E\\in \\Sigma_{II}\\cup\\Sigma_{III}, $ the norms of the transfer matrices behave like $$ e^{c_1\\gamma\\sqrt{n}}\\le\\|T_{n}(E)\\|\\le e^{c_2\\gamma\\sqrt{n}}. $$ The local dimensions of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08011","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"}