{"paper":{"title":"The existence of bound states 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":"Saidakhmat N.Lakaev, Shukhrat S.Lakaev","submitted_at":"2016-02-04T06:41:45Z","abstract_excerpt":"We consider the hamiltonian $\\mathrm{H}_{\\mu},\\mu\\in \\R$ of a system of three-particles (two identical fermions and one different particle) moving on the lattice ${\\Z}^d ,\\, d=1,2 $ interacting through repulsive $(\\mu>0)$ or attractive $(\\mu<0)$ zero-range pairwise potential $\\mu V$. We prove for any $\\mu\\ne0$ the existence of bound state of the discrete three-particle Schr\\\"odinger operator $H_{\\mu}(K),\\,K\\in \\T^d$ being the three-particle quasi-momentum, associated to the hamiltonian $\\mathrm{H}_{\\mu}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01571","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"}