{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:3DY5RIHDK7JQD4R2R2OL5I2DWU","short_pith_number":"pith:3DY5RIHD","schema_version":"1.0","canonical_sha256":"d8f1d8a0e357d301f23a8e9cbea343b50a41d71783823dabb3cf64739547ec8a","source":{"kind":"arxiv","id":"1511.02958","version":1},"attestation_state":"computed","paper":{"title":"Long-time averaged dynamics of a Bose-Einstein condensate in a bichromatic optical lattice with external harmonic confinement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.quant-gas","authors_text":"Asaad R. Sakhel","submitted_at":"2015-11-10T01:35:46Z","abstract_excerpt":"The dynamics of a Bose-Einstein condensate are examined numerically in the presence of a one-dimensional bichromatic optical lattice with external harmonic confinement. The condensate is excited by a focusing red laser. For this purpose, the time-dependent Gross Pitaevskii equation is solved using the Crank Nicolson method in real time. Two realizations of the optical lattice are considered, one with a rational and the other with an irrational ratio of the two constituting wave lengths. For a weak bichromatic optical lattice, the long-time averaged physical observables of the condensate respon"},"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":"1511.02958","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2015-11-10T01:35:46Z","cross_cats_sorted":[],"title_canon_sha256":"2c067460aac0943d5505e106eea3e08b32301e143ab8e36b7adf96d0b1fffa4a","abstract_canon_sha256":"3b284db5722d07ca23ad1769dbe207508aa43da81cbd4534d582b1ffe04d460d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:02.510194Z","signature_b64":"T9SGP98D0F4dxmwXpGblej0Q5Dz1ftuY2jLWbqMS2zK9nr0b2sq+rzxArtJ4imQOyV+wyGe0OedG4FUNdlMqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8f1d8a0e357d301f23a8e9cbea343b50a41d71783823dabb3cf64739547ec8a","last_reissued_at":"2026-05-18T01:14:02.509670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:02.509670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long-time averaged dynamics of a Bose-Einstein condensate in a bichromatic optical lattice with external harmonic confinement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.quant-gas","authors_text":"Asaad R. Sakhel","submitted_at":"2015-11-10T01:35:46Z","abstract_excerpt":"The dynamics of a Bose-Einstein condensate are examined numerically in the presence of a one-dimensional bichromatic optical lattice with external harmonic confinement. The condensate is excited by a focusing red laser. For this purpose, the time-dependent Gross Pitaevskii equation is solved using the Crank Nicolson method in real time. Two realizations of the optical lattice are considered, one with a rational and the other with an irrational ratio of the two constituting wave lengths. For a weak bichromatic optical lattice, the long-time averaged physical observables of the condensate respon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02958","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":"1511.02958","created_at":"2026-05-18T01:14:02.509757+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.02958v1","created_at":"2026-05-18T01:14:02.509757+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02958","created_at":"2026-05-18T01:14:02.509757+00:00"},{"alias_kind":"pith_short_12","alias_value":"3DY5RIHDK7JQ","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"3DY5RIHDK7JQD4R2","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"3DY5RIHD","created_at":"2026-05-18T12:29:02.477457+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/3DY5RIHDK7JQD4R2R2OL5I2DWU","json":"https://pith.science/pith/3DY5RIHDK7JQD4R2R2OL5I2DWU.json","graph_json":"https://pith.science/api/pith-number/3DY5RIHDK7JQD4R2R2OL5I2DWU/graph.json","events_json":"https://pith.science/api/pith-number/3DY5RIHDK7JQD4R2R2OL5I2DWU/events.json","paper":"https://pith.science/paper/3DY5RIHD"},"agent_actions":{"view_html":"https://pith.science/pith/3DY5RIHDK7JQD4R2R2OL5I2DWU","download_json":"https://pith.science/pith/3DY5RIHDK7JQD4R2R2OL5I2DWU.json","view_paper":"https://pith.science/paper/3DY5RIHD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.02958&json=true","fetch_graph":"https://pith.science/api/pith-number/3DY5RIHDK7JQD4R2R2OL5I2DWU/graph.json","fetch_events":"https://pith.science/api/pith-number/3DY5RIHDK7JQD4R2R2OL5I2DWU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3DY5RIHDK7JQD4R2R2OL5I2DWU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3DY5RIHDK7JQD4R2R2OL5I2DWU/action/storage_attestation","attest_author":"https://pith.science/pith/3DY5RIHDK7JQD4R2R2OL5I2DWU/action/author_attestation","sign_citation":"https://pith.science/pith/3DY5RIHDK7JQD4R2R2OL5I2DWU/action/citation_signature","submit_replication":"https://pith.science/pith/3DY5RIHDK7JQD4R2R2OL5I2DWU/action/replication_record"}},"created_at":"2026-05-18T01:14:02.509757+00:00","updated_at":"2026-05-18T01:14:02.509757+00:00"}