{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:RJGEVR6SRPZBNLWYESQD6GUCP4","short_pith_number":"pith:RJGEVR6S","schema_version":"1.0","canonical_sha256":"8a4c4ac7d28bf216aed824a03f1a827f00b3d63e3550b4c687fdd3baa496c00f","source":{"kind":"arxiv","id":"0810.4163","version":2},"attestation_state":"computed","paper":{"title":"Dispersion relation and spectral function of an impurity in a one-dimensional quantum liquid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall"],"primary_cat":"cond-mat.str-el","authors_text":"Austen Lamacraft","submitted_at":"2008-10-22T21:02:56Z","abstract_excerpt":"We consider the motion of an impurity particle in a general one-dimensional quantum fluid at zero temperature. The dispersion relation $\\Omega(P)$ of the impurity is strongly affected by interactions with the fluid as the momentum approaches $\\pm\\pi\\hbar n, \\pm 3\\pi\\hbar n, ...$, where $n$ is the density. This behavior is caused by singular $\\pm 2\\pi\\hbar n$ scattering processes and can be understood by analogy to the Kondo effect, both at strong and weak coupling, with the possibility of a quantum phase transition where $\\Omega'(\\pm \\pi n)$ jumps to zero with increasing coupling. The low ener"},"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":"0810.4163","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2008-10-22T21:02:56Z","cross_cats_sorted":["cond-mat.mes-hall"],"title_canon_sha256":"a33adf18a2c11f1dcc1686114039f0b6aac49098062f3ecb1d47afdb7795cbb5","abstract_canon_sha256":"616d6ca37702dae3f2309c71fc2ce295acfada7115dff761cabeba769fcd1616"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:09.400662Z","signature_b64":"pR9o0JSOAGgpBcRQ+o98NxxukTQ0ST8Dk6orgG8l7acK1B01iDkz7E0NuDyYo5hFnObegyY2OtcmWcabtNHMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a4c4ac7d28bf216aed824a03f1a827f00b3d63e3550b4c687fdd3baa496c00f","last_reissued_at":"2026-05-18T03:24:09.399880Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:09.399880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dispersion relation and spectral function of an impurity in a one-dimensional quantum liquid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall"],"primary_cat":"cond-mat.str-el","authors_text":"Austen Lamacraft","submitted_at":"2008-10-22T21:02:56Z","abstract_excerpt":"We consider the motion of an impurity particle in a general one-dimensional quantum fluid at zero temperature. The dispersion relation $\\Omega(P)$ of the impurity is strongly affected by interactions with the fluid as the momentum approaches $\\pm\\pi\\hbar n, \\pm 3\\pi\\hbar n, ...$, where $n$ is the density. This behavior is caused by singular $\\pm 2\\pi\\hbar n$ scattering processes and can be understood by analogy to the Kondo effect, both at strong and weak coupling, with the possibility of a quantum phase transition where $\\Omega'(\\pm \\pi n)$ jumps to zero with increasing coupling. The low ener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.4163","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":"0810.4163","created_at":"2026-05-18T03:24:09.400001+00:00"},{"alias_kind":"arxiv_version","alias_value":"0810.4163v2","created_at":"2026-05-18T03:24:09.400001+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.4163","created_at":"2026-05-18T03:24:09.400001+00:00"},{"alias_kind":"pith_short_12","alias_value":"RJGEVR6SRPZB","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"RJGEVR6SRPZBNLWY","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"RJGEVR6S","created_at":"2026-05-18T12:25:58.018023+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/RJGEVR6SRPZBNLWYESQD6GUCP4","json":"https://pith.science/pith/RJGEVR6SRPZBNLWYESQD6GUCP4.json","graph_json":"https://pith.science/api/pith-number/RJGEVR6SRPZBNLWYESQD6GUCP4/graph.json","events_json":"https://pith.science/api/pith-number/RJGEVR6SRPZBNLWYESQD6GUCP4/events.json","paper":"https://pith.science/paper/RJGEVR6S"},"agent_actions":{"view_html":"https://pith.science/pith/RJGEVR6SRPZBNLWYESQD6GUCP4","download_json":"https://pith.science/pith/RJGEVR6SRPZBNLWYESQD6GUCP4.json","view_paper":"https://pith.science/paper/RJGEVR6S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0810.4163&json=true","fetch_graph":"https://pith.science/api/pith-number/RJGEVR6SRPZBNLWYESQD6GUCP4/graph.json","fetch_events":"https://pith.science/api/pith-number/RJGEVR6SRPZBNLWYESQD6GUCP4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RJGEVR6SRPZBNLWYESQD6GUCP4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RJGEVR6SRPZBNLWYESQD6GUCP4/action/storage_attestation","attest_author":"https://pith.science/pith/RJGEVR6SRPZBNLWYESQD6GUCP4/action/author_attestation","sign_citation":"https://pith.science/pith/RJGEVR6SRPZBNLWYESQD6GUCP4/action/citation_signature","submit_replication":"https://pith.science/pith/RJGEVR6SRPZBNLWYESQD6GUCP4/action/replication_record"}},"created_at":"2026-05-18T03:24:09.400001+00:00","updated_at":"2026-05-18T03:24:09.400001+00:00"}