{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:PATTIBOX5LNR4UJWNECWW7TZOO","short_pith_number":"pith:PATTIBOX","schema_version":"1.0","canonical_sha256":"78273405d7eadb1e513669056b7e79738f885dc76ecbb9086c32d9add7938a0f","source":{"kind":"arxiv","id":"0910.2341","version":1},"attestation_state":"computed","paper":{"title":"Detailed analysis of quantum phase transitions within the $u(2)$ algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nucl-th","authors_text":"L.Fortunato, L.Sartori","submitted_at":"2009-10-13T09:21:39Z","abstract_excerpt":"We analyze in detail the quantum phase transitions that arise in models based on the $u(2)$ algebraic description for bosonic systems with two types of scalar bosons. First we discuss the quantum phase transition that occurs in hamiltonians that admix the two dynamical symmetry chains $u(2)\\supset u(1)$ and $u(2)\\supset so(2)$ by diagonalizing the problem exactly in the $u(1)$ basis. Then we apply the coherent state formalism to determine the energy functional. Finally we show that a quantum phase transition of a different nature, but displaying similar characteristics, may arise also within a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0910.2341","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nucl-th","submitted_at":"2009-10-13T09:21:39Z","cross_cats_sorted":[],"title_canon_sha256":"f0f64344b98dc4d0f050d61ea84ba0ef60ea7f3630b4ff1ea0367329e2e4d384","abstract_canon_sha256":"5b4af928520780d8dd720864ec9758f9840ae3d4f43d16be1d9db2be999b1d65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:19.111136Z","signature_b64":"XALVSQk/K0ifYRksGPfGjTA31dRORUX8N6vlOcN7MN5u8n3hzCPrndHD0GcVFxfOz7rT00LJBftSnhRz1P4mDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78273405d7eadb1e513669056b7e79738f885dc76ecbb9086c32d9add7938a0f","last_reissued_at":"2026-05-18T02:34:19.110576Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:19.110576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Detailed analysis of quantum phase transitions within the $u(2)$ algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nucl-th","authors_text":"L.Fortunato, L.Sartori","submitted_at":"2009-10-13T09:21:39Z","abstract_excerpt":"We analyze in detail the quantum phase transitions that arise in models based on the $u(2)$ algebraic description for bosonic systems with two types of scalar bosons. First we discuss the quantum phase transition that occurs in hamiltonians that admix the two dynamical symmetry chains $u(2)\\supset u(1)$ and $u(2)\\supset so(2)$ by diagonalizing the problem exactly in the $u(1)$ basis. Then we apply the coherent state formalism to determine the energy functional. Finally we show that a quantum phase transition of a different nature, but displaying similar characteristics, may arise also within a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2341","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0910.2341","created_at":"2026-05-18T02:34:19.110665+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.2341v1","created_at":"2026-05-18T02:34:19.110665+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2341","created_at":"2026-05-18T02:34:19.110665+00:00"},{"alias_kind":"pith_short_12","alias_value":"PATTIBOX5LNR","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"PATTIBOX5LNR4UJW","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"PATTIBOX","created_at":"2026-05-18T12:26:01.383474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PATTIBOX5LNR4UJWNECWW7TZOO","json":"https://pith.science/pith/PATTIBOX5LNR4UJWNECWW7TZOO.json","graph_json":"https://pith.science/api/pith-number/PATTIBOX5LNR4UJWNECWW7TZOO/graph.json","events_json":"https://pith.science/api/pith-number/PATTIBOX5LNR4UJWNECWW7TZOO/events.json","paper":"https://pith.science/paper/PATTIBOX"},"agent_actions":{"view_html":"https://pith.science/pith/PATTIBOX5LNR4UJWNECWW7TZOO","download_json":"https://pith.science/pith/PATTIBOX5LNR4UJWNECWW7TZOO.json","view_paper":"https://pith.science/paper/PATTIBOX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.2341&json=true","fetch_graph":"https://pith.science/api/pith-number/PATTIBOX5LNR4UJWNECWW7TZOO/graph.json","fetch_events":"https://pith.science/api/pith-number/PATTIBOX5LNR4UJWNECWW7TZOO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PATTIBOX5LNR4UJWNECWW7TZOO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PATTIBOX5LNR4UJWNECWW7TZOO/action/storage_attestation","attest_author":"https://pith.science/pith/PATTIBOX5LNR4UJWNECWW7TZOO/action/author_attestation","sign_citation":"https://pith.science/pith/PATTIBOX5LNR4UJWNECWW7TZOO/action/citation_signature","submit_replication":"https://pith.science/pith/PATTIBOX5LNR4UJWNECWW7TZOO/action/replication_record"}},"created_at":"2026-05-18T02:34:19.110665+00:00","updated_at":"2026-05-18T02:34:19.110665+00:00"}