{"paper":{"title":"Two phases of the noncommutative quantum mechanics","license":"","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"Armen Nersessian, Corneliu Sochichiu, Stefano Bellucci","submitted_at":"2001-06-15T15:25:50Z","abstract_excerpt":"We consider quantum mechanics on the noncommutative plane in the presence of magnetic field $B$. We show, that the model has two essentially different phases separated by the point $B\\theta=c\\hbar^2/e$, where $\\theta$ is a parameter of noncommutativity. In this point the system reduces to exactly-solvable one-dimensional system. When $\\kappa=1-eB\\theta/c\\hbar^2<0$ there is a finite number of states corresponding to the given value of the angular momentum. In another phase, i.e. when $\\kappa>0$ the number of states is infinite. The perturbative spectrum near the critical point $\\kappa=0$ is com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0106138","kind":"arxiv","version":4},"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"}