{"paper":{"title":"On the existence of impurity bound excitons in one-dimensional systems with zero range interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Horia D. Cornean, Hynek Kovarik, Jonas Have, Thomas G. Pedersen","submitted_at":"2017-01-16T14:32:26Z","abstract_excerpt":"We consider a three-body one-dimensional Schr\\\"odinger operator with zero range potentials, which models a positive impurity with charge $\\kappa > 0$ interacting with an exciton. We study the existence of discrete eigenvalues as $\\kappa$ is varied. On one hand, we show that for sufficiently small $\\kappa$ there exists a unique bound state whose binding energy behaves like $\\kappa^4$, and we explicitly compute its leading coefficient. On the other hand, if $\\kappa$ is larger than some critical value then the system has no bound states."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04302","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"}