{"paper":{"title":"Anderson localization for one-frequency quasi-periodic block operators with long-range interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.SP","authors_text":"Wenwen Jian, Xiaoping Yuan, Yunfeng Shi","submitted_at":"2017-11-23T11:43:31Z","abstract_excerpt":"In this paper, we study the quasi-periodic operators $H_{\\epsilon,\\omega}(x)$: $$(H_{\\epsilon,\\omega}(x)\\vec{\\psi})_n=\\epsilon\\sum_{k\\in\\mathbb{Z}}W_k\\vec{\\psi}_{n-k}+V(x+n\\omega)\\vec{\\psi}_n,$$ where $$\\vec{\\psi}=\\{\\vec{\\psi}_n\\}\\in\\ell^2(\\mathbb{Z},\\mathbb{C}^l),\\ V(x)=\\text{diag}\\left(v_1(x),\\cdots,v_l(x)\\right)$$ with $v_i$ ($1\\leq i \\leq l$) being real analytic functions on $\\mathbb{T}=\\mathbb{R}/\\mathbb{Z}$ and $W_k$ ($k\\in\\mathbb{Z}$) being $l\\times l$ matrices satisfying $\\|W_k\\|\\leq C_0e^{-\\rho|k|}$. Using techniques developed by Bourgain and Goldstein [\\textit{{Ann. of Math. 152(3):8"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08661","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"}