{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:IP2EEU44TV565JMYIB2NHBTGZ2","short_pith_number":"pith:IP2EEU44","schema_version":"1.0","canonical_sha256":"43f442539c9d7beea5984074d38666ce84169584d6910eddadc4298f33ca7917","source":{"kind":"arxiv","id":"1011.3140","version":2},"attestation_state":"computed","paper":{"title":"Phase transition to Bose-Einstein condensation for a Bosonic gas confined in a combined trap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.atom-ph"],"primary_cat":"cond-mat.quant-gas","authors_text":"Baolong L\\\"u, Bing Wang, Hongwei Xiong, Lijuan Cao, Xinzhou Tan","submitted_at":"2010-11-13T14:52:38Z","abstract_excerpt":"We present a study of phase transition to macroscopic superfluidity for an ultracold bosonic gas confined in a combined trap formed by a one-dimensional optical lattice and a harmonic potential, focusing on the critical temperature of this system and the interference patterns of the Bose gas released from the combined trap. Based on a semiclassical energy spectrum, we develop an analytic approximation for the critical temperature $T_{c}$, and compare the analytic results with that obtained by numerical computations. For finite temperatures below $T_{c}$, we calculate the interference patterns "},"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":"1011.3140","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2010-11-13T14:52:38Z","cross_cats_sorted":["physics.atom-ph"],"title_canon_sha256":"0fa8c783ac2bfbda0f56867d6e7dfadeb2a342af144977b2715ccd8bc3e6e389","abstract_canon_sha256":"8278f6b7a3ad7634eb1a844844077b957b4cf95a0176818ec16d31f171c93365"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:47.947916Z","signature_b64":"4w2vOHoRrsb8dO7AFmDJFP9dGi9Zv0HE/CNa+t4GivvPiwRcKIRX/S1582KYFxUruNtYwA4JBJWuFPUasiIuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43f442539c9d7beea5984074d38666ce84169584d6910eddadc4298f33ca7917","last_reissued_at":"2026-05-18T02:04:47.947112Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:47.947112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase transition to Bose-Einstein condensation for a Bosonic gas confined in a combined trap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.atom-ph"],"primary_cat":"cond-mat.quant-gas","authors_text":"Baolong L\\\"u, Bing Wang, Hongwei Xiong, Lijuan Cao, Xinzhou Tan","submitted_at":"2010-11-13T14:52:38Z","abstract_excerpt":"We present a study of phase transition to macroscopic superfluidity for an ultracold bosonic gas confined in a combined trap formed by a one-dimensional optical lattice and a harmonic potential, focusing on the critical temperature of this system and the interference patterns of the Bose gas released from the combined trap. Based on a semiclassical energy spectrum, we develop an analytic approximation for the critical temperature $T_{c}$, and compare the analytic results with that obtained by numerical computations. For finite temperatures below $T_{c}$, we calculate the interference patterns "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3140","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1011.3140","created_at":"2026-05-18T02:04:47.947231+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.3140v2","created_at":"2026-05-18T02:04:47.947231+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3140","created_at":"2026-05-18T02:04:47.947231+00:00"},{"alias_kind":"pith_short_12","alias_value":"IP2EEU44TV56","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"IP2EEU44TV565JMY","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"IP2EEU44","created_at":"2026-05-18T12:26:09.077623+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/IP2EEU44TV565JMYIB2NHBTGZ2","json":"https://pith.science/pith/IP2EEU44TV565JMYIB2NHBTGZ2.json","graph_json":"https://pith.science/api/pith-number/IP2EEU44TV565JMYIB2NHBTGZ2/graph.json","events_json":"https://pith.science/api/pith-number/IP2EEU44TV565JMYIB2NHBTGZ2/events.json","paper":"https://pith.science/paper/IP2EEU44"},"agent_actions":{"view_html":"https://pith.science/pith/IP2EEU44TV565JMYIB2NHBTGZ2","download_json":"https://pith.science/pith/IP2EEU44TV565JMYIB2NHBTGZ2.json","view_paper":"https://pith.science/paper/IP2EEU44","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.3140&json=true","fetch_graph":"https://pith.science/api/pith-number/IP2EEU44TV565JMYIB2NHBTGZ2/graph.json","fetch_events":"https://pith.science/api/pith-number/IP2EEU44TV565JMYIB2NHBTGZ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IP2EEU44TV565JMYIB2NHBTGZ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IP2EEU44TV565JMYIB2NHBTGZ2/action/storage_attestation","attest_author":"https://pith.science/pith/IP2EEU44TV565JMYIB2NHBTGZ2/action/author_attestation","sign_citation":"https://pith.science/pith/IP2EEU44TV565JMYIB2NHBTGZ2/action/citation_signature","submit_replication":"https://pith.science/pith/IP2EEU44TV565JMYIB2NHBTGZ2/action/replication_record"}},"created_at":"2026-05-18T02:04:47.947231+00:00","updated_at":"2026-05-18T02:04:47.947231+00:00"}