Pith Number

pith:H74PVXSH

pith:2026:H74PVXSHUDJDHSNTIJ73US7F6V

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On the asymptotic behavior at the kinetic time of a weakly interacting Fermi gas

Herbert Spohn, Minh-Binh Tran, Peter S. Madsen, Phan Th\`anh Nam

For a weakly interacting Fermi gas starting near equilibrium, the leading decay of two-point time correlations at kinetic times is fixed exactly by the collision frequency of the Boltzmann-Nordheim operator.

arxiv:2605.13499 v1 · 2026-05-13 · math-ph · math.MP

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Claims

C1strongest claim

we show that its leading order behavior is determined completely by the collisional frequency of the Boltzmann-Nordheim collision operator at equilibrium. This settles a prediction by Lukkarinen-Spohn, and thus gives a justification of the quantum Boltzmann equation from many-body quantum mechanics.

C2weakest assumption

The initial state is close to equilibrium; the interaction strength λ is small, and the analysis is restricted to the kinetic time regime t ∼ λ^{-2}.

C3one line summary

The leading-order asymptotic behavior of the two-point correlation function for a weakly interacting Fermi gas at kinetic times is exactly the collisional frequency of the equilibrium Boltzmann-Nordheim collision operator.

References

21 extracted · 21 resolved · 0 Pith anchors

[1] R. Balescu. Equilibrium and nonequilibrium statistical mechanics.NASA STI Recon Technical Report A, 76, 1975 1975

[2] Y. Deng and Z. Hani. Full derivation of the wave kinetic equation.Inventiones Mathematicae, 233(2):543–724, 2023 2023

[3] Y. Deng and Z. Hani. Long time justification of wave turbulence theory. arXiv e-print, arXiv:2311.10082, 2023 2023

[4] Long time derivation of the boltzmann equation from hard sphere dynamics 2025

[5] L. Erd¨ os, M. Salmhofer, and H.-T. Yau. On the quantum boltzmann equation.Journal of Statistical Physics, 116:367–380, 08 2004 2004

Receipt and verification

First computed	2026-05-18T02:44:41.028358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ff8fade47a0d233c9b3427fba4be5f56839de3ac572183878edbcf8fb031e24

Aliases

arxiv: 2605.13499 · arxiv_version: 2605.13499v1 · doi: 10.48550/arxiv.2605.13499 · pith_short_12: H74PVXSHUDJD · pith_short_16: H74PVXSHUDJDHSNT · pith_short_8: H74PVXSH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/H74PVXSHUDJDHSNTIJ73US7F6V \
  | 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: 3ff8fade47a0d233c9b3427fba4be5f56839de3ac572183878edbcf8fb031e24

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05f59411bd7b71c8038051c09d80d08317a840ba27ef6255f7e76e947291feee",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-13T13:21:43Z",
    "title_canon_sha256": "1cae84d075ed6cb05215cd0a7d2f41aeba15ad68b8174bda56fc466414088a69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13499",
    "kind": "arxiv",
    "version": 1
  }
}