{"paper":{"title":"Large-$N$ scaling of Tan's contact for the harmonically trapped Tonks--Girardeau gas at finite temperature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"In the large-N limit the subleading coefficient of Tan's contact for trapped Tonks-Girardeau bosons is given by universal phase-space integrals of the Fermi factor and equals the canonical-grand-canonical ensemble difference at fixed mean N","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.quant-gas","authors_text":"Felipe Taha Sant'Ana","submitted_at":"2026-05-15T14:25:36Z","abstract_excerpt":"We derive the canonical-ensemble scaling of Tan's contact for $N$ harmonically trapped Tonks--Girardeau bosons at finite temperature in the large-$N$ limit. The leading scaling coefficient reproduces the local-density-approximation result and is obtained from a contour-integral representation of the canonical partition function followed by a saddle-point reduction to a phase-space integral with a self-consistent scaled chemical potential. The subleading coefficient is the central new object of this work: it admits an explicit representation in terms of universal phase-space integrals of the Fe"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The subleading coefficient in the large-N scaling of Tan's contact admits an explicit representation in terms of universal phase-space integrals of the Fermi factor, has closed-form Sommerfeld and virial limits, and is identified with the canonical-versus-grand-canonical ensemble difference at fixed mean particle number.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The saddle-point reduction of the contour-integral representation of the canonical partition function to a phase-space integral with a self-consistent scaled chemical potential remains accurate across the full temperature range for large but finite N.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Derives leading and subleading large-N scaling coefficients for Tan's contact in the trapped Tonks-Girardeau gas at finite temperature via saddle-point analysis of the canonical partition function, with Padé approximants and numerical verification.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"In the large-N limit the subleading coefficient of Tan's contact for trapped Tonks-Girardeau bosons is given by universal phase-space integrals of the Fermi factor and equals the canonical-grand-canonical ensemble difference at fixed mean N","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2499b1989b26e5b0757a38fb585ebd5448faa380c7c04fa845973ed7ea91efd6"},"source":{"id":"2605.15994","kind":"arxiv","version":1},"verdict":{"id":"f4f90b21-2e1a-4912-80ab-e031ac68baa5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:09:14.810172Z","strongest_claim":"The subleading coefficient in the large-N scaling of Tan's contact admits an explicit representation in terms of universal phase-space integrals of the Fermi factor, has closed-form Sommerfeld and virial limits, and is identified with the canonical-versus-grand-canonical ensemble difference at fixed mean particle number.","one_line_summary":"Derives leading and subleading large-N scaling coefficients for Tan's contact in the trapped Tonks-Girardeau gas at finite temperature via saddle-point analysis of the canonical partition function, with Padé approximants and numerical verification.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The saddle-point reduction of the contour-integral representation of the canonical partition function to a phase-space integral with a self-consistent scaled chemical potential remains accurate across the full temperature range for large but finite N.","pith_extraction_headline":"In the large-N limit the subleading coefficient of Tan's contact for trapped Tonks-Girardeau bosons is given by universal phase-space integrals of the Fermi factor and equals the canonical-grand-canonical ensemble difference at fixed mean N"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15994/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:19.026721Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:20:53.493452Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:42.179290Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:01:55.664792Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"9f092790642b8a07543138a1a313843f76e666588cf0f11358fb6d33e9096bb7"},"references":{"count":45,"sample":[{"doi":"","year":null,"title":"Tan S 2008Ann. 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