{"paper":{"title":"The existence of an isolated band in a system of three particles in an optical lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Ahmad M. Khalkhuzhaev, Gianfausto Dell'Antonio, Saidakhmat N. Lakaev","submitted_at":"2015-12-07T11:15:02Z","abstract_excerpt":"We prove the existence of two-and three-particle bound states of the Schr\\\"odinger operators $h_\\mu(k),k\\in \\T^d$ and $H_\\mu(K),K\\in \\T^d$ associated to Hamiltonians $\\mathrm{h}_{\\mu}$ and $\\mathrm{H}_{\\mu}$ of a system of two and three identical bosons on the lattice $\\Z^d, d=1,2$ interacting via pairwise zero-range attractive $\\mu<0$ or repulsive $\\mu>0$ potentials. As a consequence we show the existence of an isolated band in the two and three bosonic systems in an optical lattice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01983","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"}