Pith Number

pith:K2OKFXJ4

pith:2026:K2OKFXJ4HTZO4BHLHY3AWWHXQC

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Large-$N$ scaling of Tan's contact for the harmonically trapped Tonks--Girardeau gas at finite temperature

Felipe Taha Sant'Ana

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

arxiv:2605.15994 v1 · 2026-05-15 · cond-mat.quant-gas · cond-mat.stat-mech

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

45 extracted · 45 resolved · 0 Pith anchors

[1] Tan S 2008Ann. Phys. (N.Y.)3232952–2970

[2] Tan S 2008Ann. Phys. (N.Y.)3232971–2986

[3] Tan S 2008Ann. Phys. (N.Y.)3232987–2990

[4] Braaten E and Platter L 2008Phys. Rev. Lett.100205301

[5] Braaten E, Kang D and Platter L 2011Phys. Rev. Lett.106153005

Receipt and verification

First computed	2026-05-20T00:01:48.174766Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

569ca2dd3c3cf2ee04eb3e360b58f780b7c77511e7181e6d9056cf378fbe3cf1

Aliases

arxiv: 2605.15994 · arxiv_version: 2605.15994v1 · doi: 10.48550/arxiv.2605.15994 · pith_short_12: K2OKFXJ4HTZO · pith_short_16: K2OKFXJ4HTZO4BHL · pith_short_8: K2OKFXJ4

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/K2OKFXJ4HTZO4BHLHY3AWWHXQC \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 569ca2dd3c3cf2ee04eb3e360b58f780b7c77511e7181e6d9056cf378fbe3cf1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd41a56ed285c3509fa38ab6a7229b442939662d971ef02513dbc7f999b44091",
    "cross_cats_sorted": [
      "cond-mat.stat-mech"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.quant-gas",
    "submitted_at": "2026-05-15T14:25:36Z",
    "title_canon_sha256": "a32654a23ba35d7040a54568939b4d276843a99415c7d150fb5d02888ad68d42"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15994",
    "kind": "arxiv",
    "version": 1
  }
}