Pith Number

pith:34ON52V2

pith:2026:34ON52V2RSF4WEBZLB4OZJCJIX

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Operator ordering as an emergent geometric background in Dirac systems with spatially varying mass

C. A. S. Almeida

Consistent Hermitian ordering of the Dirac operator with spatially varying mass adds a logarithmic-gradient term that shifts discrete spectra in a mode-dependent way.

arxiv:2605.14148 v1 · 2026-05-13 · cond-mat.mes-hall · quant-ph

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Claims

C1strongest claim

The consistent relativistic ordering of the Dirac operator leads to observable modifications of discrete spectra in spatially inhomogeneous scalar backgrounds, with a mode-dependent second-order spectral shift strongly enhanced near the mass-inversion threshold.

C2weakest assumption

That probability-current conservation uniquely fixes the Hermitian ordering of the Dirac Hamiltonian with spatially varying mass, with no other admissible prescriptions existing in the relativistic case.

C3one line summary

Unique Hermitian ordering of the Dirac operator with spatially varying mass generates a logarithmic-gradient correction that induces mode-dependent second-order shifts in the discrete spectrum.

References

20 extracted · 20 resolved · 0 Pith anchors

[1] R. Jackiw, C. Rebbi, Solitons with fermion number1/2,Phys. Rev. D13(1976) 3398– 3409 1976

[2] A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, The electronic properties of graphene,Rev. Mod. Phys.81(2009) 109–162 2009

[3] M. A. H. Vozmediano, M. I. Katsnelson, F. Guinea, Gauge fields in graphene,Phys. Rep.496(2010) 109–148 2010

[4] K. Chen, F. Komissarenko, D. Smirnova, A. Vakulenko, S. Kiriushechkina, I. Volkovskaya, S. Guddala, V. Menon, A. Alù, A. B. Khanikaev, Photonic Dirac cavities with spatially varying mass term,Sci. Adv 2023

[5] S. Kim, K. Kim, Spatial localization and diffusion of Dirac particles and waves induced by random temporal medium variations,Commun. Phys.8(2025) 32 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:11.607375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df1cdeeaba8c8bcb10395878eca44945cfabda5cf08a8309210c78b2fc9ed8e4

Aliases

arxiv: 2605.14148 · arxiv_version: 2605.14148v1 · doi: 10.48550/arxiv.2605.14148 · pith_short_12: 34ON52V2RSF4 · pith_short_16: 34ON52V2RSF4WEBZ · pith_short_8: 34ON52V2

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/34ON52V2RSF4WEBZLB4OZJCJIX \
  | 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: df1cdeeaba8c8bcb10395878eca44945cfabda5cf08a8309210c78b2fc9ed8e4

Canonical record JSON

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    "abstract_canon_sha256": "4f5242eb8cbed17ee871dc539c7f14d0c3eb834c432d4a3c58a4979010ba39a9",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.mes-hall",
    "submitted_at": "2026-05-13T21:59:17Z",
    "title_canon_sha256": "96e48c93754e2bb577569e02ac6203c2373bcf47f0aad0e81a1cc4bad420027d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14148",
    "kind": "arxiv",
    "version": 1
  }
}