Pith Number

pith:6K7MVPSI

pith:2025:6K7MVPSIXM7CEIFPTCNXVFZLZW

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Coexistence of Anderson Localization and Quantum Scarring in Two Dimensions

Anant Vijay Varma, Esa R\"as\"anen, Fartash Chalangari, Joonas Keski-Rahkonen

Finite two-dimensional disordered systems host both Anderson-localized states at low energy and scarred states at higher energy.

arxiv:2512.20788 v3 · 2025-12-23 · quant-ph

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Claims

C1strongest claim

We demonstrate that this coexistence produces distinct, robust signatures in both spatial intensity patterns and spectral statistics that are directly observable in mesoscopic electronic, photonic, and cold-atom systems.

C2weakest assumption

Scaling theory predicts that in two dimensions all eigenstates localize in the large-system-size limit, yet the energy-dependent localization length and finite-size effects allow these regimes to coexist.

C3one line summary

In finite 2D disordered systems, Anderson localization at low energies coexists with quantum scarring at higher energies due to energy-dependent localization lengths and finite-size effects, producing observable signatures in intensity patterns and spectral statistics.

References

55 extracted · 55 resolved · 0 Pith anchors

[1] De Tomasi and I 2020

[2] B. L. Altshuler, E. Cuevas, L. B. Ioffe, and V. E. Kravtsov, Nonergodic phases in strongly disordered ran- dom regular graphs, Physical Review Letters117, 156601 (2016) 2016

[3] A. K. Das, A. Ghosh, and I. M. Khaymovich, Emergent multifractality in power-law decaying eigenstates, Physi- cal Review B112, 024201 (2025) 2025

[4] W.-F. Xu and W. J. Rao, Non-ergodic extended regime in random matrix ensembles: insights from eigenvalue spectra, Scientific Reports13, 27751 (2023) 2023

[5] P. W. Anderson, Absence of diffusion in certain random lattices, Physical Review109, 1492–1505 (1958) 1958

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-28T01:04:34.662475Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2becabe48bb3e2220af989b7a972bcda87367ea98fb805de9330aec6f330e82

Aliases

arxiv: 2512.20788 · arxiv_version: 2512.20788v3 · doi: 10.48550/arxiv.2512.20788 · pith_short_12: 6K7MVPSIXM7C · pith_short_16: 6K7MVPSIXM7CEIFP · pith_short_8: 6K7MVPSI

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6K7MVPSIXM7CEIFPTCNXVFZLZW \
  | 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: f2becabe48bb3e2220af989b7a972bcda87367ea98fb805de9330aec6f330e82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6518fe55b08b5120f4034c18289e8d45e53c0dbc6619b9d3f6fdb6cc81c021e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-12-23T21:35:57Z",
    "title_canon_sha256": "738e6c7168c58c4544e5bbd0f589293f2fa61184c7b953f77a68b11d5695253e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.20788",
    "kind": "arxiv",
    "version": 3
  }
}