{"paper":{"title":"Stark-Wannier Ladders and Cubic Exponential Sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexander Fedotov, Fr\\'ed\\'eric Klopp (IMJ-PRG)","submitted_at":"2016-04-22T14:49:42Z","abstract_excerpt":"On L 2 (R), we consider the Schr\\\"odinger operator (1.1) H \\k{o} = -- $\\partial$ 2 $\\partial$x 2 + v(x) -- \\k{o}x, where v is a real analytic 1-periodic function and \\k{o} is a positive constant. This operator is a model to study a Bloch electron in a constant electric field ([1]). The parameter \\k{o} is proportional to the electric field. The operator (1.1) was studied both by physicists (see, e.g., the review [6]) and by mathematicians (see, e.g., [9]). Its spectrum is absolutely continuous and fills the real axis. One of main features of H \\k{o} is the existence of Stark-Wannier ladders. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06690","kind":"arxiv","version":1},"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"}