Pith Number

pith:VPIWTK2T

pith:2022:VPIWTK2TTJC3HLZ5CTYGVJ6HRJ

not attested not anchored not stored refs pending

Emergent Wigner-Dyson Statistics and Self-Attention-Based Prediction in Driven Bose-Hubbard Chains

Chen-Huan Wu

A self-attention algorithm on driven Bose-Hubbard chains produces many-body spectra whose level statistics sit between the Gaussian Symplectic and Gaussian Unitary ensembles according to the ratio U/J.

arxiv:2208.01303 v11 · 2022-08-02 · cond-mat.stat-mech

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Record completeness

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Claims

C1strongest claim

The resulting system follows statistics intermediate between the Gaussian Symplectic Ensemble (GSE) and Gaussian Unitary Ensemble (GUE), contingent on the ratio U/J. Our algorithm allows for the automatic optimization and prediction of the resulting many-body spectrum to arbitrary accuracy, revealing non-Fermi liquid-like behavior in the strongly interacting bosonic phase.

C2weakest assumption

That the Gaussian-based self-attention mapping to high-dimensional feature space, with flavor number O(M) set by the local Kerr potential difference 1/2 U, faithfully reproduces the chaotic many-body spectrum and level statistics without requiring explicit verification against exact diagonalization on accessible system sizes.

C3one line summary

A replica-inspired algorithm with Gaussian self-attention predicts many-body spectra in driven Bose-Hubbard chains and reports statistics intermediate between GSE and GUE depending on U/J.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-27T01:04:46.083270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abd169ab539a45b3af3d14f06aa7c78a458ebbfa99ba698d2d48527141e4e009

Aliases

arxiv: 2208.01303 · arxiv_version: 2208.01303v11 · doi: 10.48550/arxiv.2208.01303 · pith_short_12: VPIWTK2TTJC3 · pith_short_16: VPIWTK2TTJC3HLZ5 · pith_short_8: VPIWTK2T

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VPIWTK2TTJC3HLZ5CTYGVJ6HRJ \
  | 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: abd169ab539a45b3af3d14f06aa7c78a458ebbfa99ba698d2d48527141e4e009

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "985679f0d07b55b2e041a49382376af654d3b58114dfe55ef7e1e9eab5676b3b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2022-08-02T08:15:14Z",
    "title_canon_sha256": "25404d12dd688d8bbc028b5dac6ecadfc00da456238b237da12556be9a1a87d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2208.01303",
    "kind": "arxiv",
    "version": 11
  }
}