{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:PAOKJ7WRX5RUHXKASUMZS6Q34P","short_pith_number":"pith:PAOKJ7WR","schema_version":"1.0","canonical_sha256":"781ca4fed1bf6343dd409519997a1be3c78ebdf0440fe8e691c5c1957dc1254f","source":{"kind":"arxiv","id":"1212.0708","version":1},"attestation_state":"computed","paper":{"title":"Correlations in non-equilibrium Luttinger liquid and singular Fredholm determinants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math-ph","math.MP"],"primary_cat":"cond-mat.str-el","authors_text":"A. D. Mirlin, D. B. Gutman, I. V. Protopopov","submitted_at":"2012-12-04T12:59:53Z","abstract_excerpt":"We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants ${\\rm det}(1+\\hat{A}\\hat{B})$, where $A(\\epsilon)$ and $B(t)$ have multiple discontinuities in energy and time spaces. Such determinants are a generalization of Toeplitz determinants with Fisher-Hartwig singularities. We propose a general asymptotic formula for this class of determinants and provide analytical and numerical support to this conjecture. This allows us to establish non-equilibrium power-law singularities of ma"},"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":"1212.0708","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2012-12-04T12:59:53Z","cross_cats_sorted":["cond-mat.mes-hall","math-ph","math.MP"],"title_canon_sha256":"6bfb54b04091ca3e191d7b015aa0cbd11035385696e90ccaf6bb12d011d6251c","abstract_canon_sha256":"b7e6b233ca8cc8ad4f6c464035ed1f93cb53abd8216a442268dfe388797aff05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:47.934471Z","signature_b64":"uava0MH+bzpHxhz2KU+qAKjGA5rTQTRCW86sPfbmvY8H3+7jAzQ6OQIKXmANu+SUBjlwaGy9I8Wi+dBDCIYaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"781ca4fed1bf6343dd409519997a1be3c78ebdf0440fe8e691c5c1957dc1254f","last_reissued_at":"2026-05-18T01:52:47.934117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:47.934117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Correlations in non-equilibrium Luttinger liquid and singular Fredholm determinants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math-ph","math.MP"],"primary_cat":"cond-mat.str-el","authors_text":"A. D. Mirlin, D. B. Gutman, I. V. Protopopov","submitted_at":"2012-12-04T12:59:53Z","abstract_excerpt":"We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants ${\\rm det}(1+\\hat{A}\\hat{B})$, where $A(\\epsilon)$ and $B(t)$ have multiple discontinuities in energy and time spaces. Such determinants are a generalization of Toeplitz determinants with Fisher-Hartwig singularities. We propose a general asymptotic formula for this class of determinants and provide analytical and numerical support to this conjecture. This allows us to establish non-equilibrium power-law singularities of ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0708","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":"1212.0708","created_at":"2026-05-18T01:52:47.934170+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.0708v1","created_at":"2026-05-18T01:52:47.934170+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0708","created_at":"2026-05-18T01:52:47.934170+00:00"},{"alias_kind":"pith_short_12","alias_value":"PAOKJ7WRX5RU","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"PAOKJ7WRX5RUHXKA","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"PAOKJ7WR","created_at":"2026-05-18T12:27:18.751474+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/PAOKJ7WRX5RUHXKASUMZS6Q34P","json":"https://pith.science/pith/PAOKJ7WRX5RUHXKASUMZS6Q34P.json","graph_json":"https://pith.science/api/pith-number/PAOKJ7WRX5RUHXKASUMZS6Q34P/graph.json","events_json":"https://pith.science/api/pith-number/PAOKJ7WRX5RUHXKASUMZS6Q34P/events.json","paper":"https://pith.science/paper/PAOKJ7WR"},"agent_actions":{"view_html":"https://pith.science/pith/PAOKJ7WRX5RUHXKASUMZS6Q34P","download_json":"https://pith.science/pith/PAOKJ7WRX5RUHXKASUMZS6Q34P.json","view_paper":"https://pith.science/paper/PAOKJ7WR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.0708&json=true","fetch_graph":"https://pith.science/api/pith-number/PAOKJ7WRX5RUHXKASUMZS6Q34P/graph.json","fetch_events":"https://pith.science/api/pith-number/PAOKJ7WRX5RUHXKASUMZS6Q34P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PAOKJ7WRX5RUHXKASUMZS6Q34P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PAOKJ7WRX5RUHXKASUMZS6Q34P/action/storage_attestation","attest_author":"https://pith.science/pith/PAOKJ7WRX5RUHXKASUMZS6Q34P/action/author_attestation","sign_citation":"https://pith.science/pith/PAOKJ7WRX5RUHXKASUMZS6Q34P/action/citation_signature","submit_replication":"https://pith.science/pith/PAOKJ7WRX5RUHXKASUMZS6Q34P/action/replication_record"}},"created_at":"2026-05-18T01:52:47.934170+00:00","updated_at":"2026-05-18T01:52:47.934170+00:00"}