{"paper":{"title":"Asymptotics of Eigenvalues of the Two-particle Schr\\\"{o}dinger operators on lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Saidakhmat N. Lakaev, Shohruh Yu. Holmatov","submitted_at":"2010-10-12T10:39:52Z","abstract_excerpt":"The Hamiltonian of a system of two quantum mechanical particles moving on the $d$-dimensional lattice $\\Z^d$ and interacting via zero-range attractive pair potentials is considered. For the two-particle energy operator $H_{\\mu}(K),$ $K\\in \\T^d=(-\\pi,\\pi]^d$ -- the two-particle quasi-momentum, the existence of a unique positive eigenvalue $z(\\mu, K)$ above the upper edge of the essential spectrum of $H_{\\mu}(K)$ is proven and asymptotics for $z(\\mu, K)$ are found when $\\mu$ approaches to some $\\mu_0(K)$ and $K\\to 0.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2348","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"}