Pith Number

pith:M4IX4AAQ

pith:2026:M4IX4AAQCFQVNZEK4NN5QNLNH5

not attested not anchored not stored refs resolved

Nonlocal Optical Response and Surface Susceptibilities: A Systematic Derivation via Spatial Moment Expansion

Fr\'ed\'eric Zolla

Nonlocal optical response at curved interfaces condenses into a single surface susceptibility scalar at leading order.

arxiv:2605.15716 v1 · 2026-05-15 · physics.optics · cond-mat.mes-hall · math-ph · math.MP

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Claims

C1strongest claim

Starting from the most general tensorial nonlocal constitutive relation and combining a spatial moment expansion with a distributional thin-layer limit, we show that the full complexity of the interfacial response condenses, at leading order, into a single scalar: the surface susceptibility χ^s, equal for the tangential and normal components of the electric field. These quantities provide a constructive generalization of the Feibelman d-parameters to interfaces of arbitrary curvature, and the curvature corrections, proportional to the geometric invariants H (mean curvature) and K (Gaussian curvature), are derived explicitly.

C2weakest assumption

The distributional thin-layer limit applied after the spatial moment expansion is sufficient to capture the leading-order interfacial response, with higher-order contributions negligible for the condensation to a single scalar χ^s and the explicit curvature corrections.

C3one line summary

Nonlocal response kernels for homogeneous media condense at leading order into a single scalar surface susceptibility χ^s (equal for tangential and normal fields) with explicit curvature corrections proportional to mean curvature H and Gaussian curvature K.

References

2 extracted · 2 resolved · 0 Pith anchors

[1] Electronic excitations: density-functional versus many-body green’s-function approaches 1999 · doi:10.1017/cbo9781139644181

[2] On the vibrations of the electronic plasma 2004 · doi:10.1007/978-3-0348-7966-8

Formal links

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Receipt and verification

First computed	2026-05-20T00:01:14.373204Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67117e0010116156e48ae35bd8356d3f6befc912ae31a7727770a0164b37403b

Aliases

arxiv: 2605.15716 · arxiv_version: 2605.15716v1 · doi: 10.48550/arxiv.2605.15716 · pith_short_12: M4IX4AAQCFQV · pith_short_16: M4IX4AAQCFQVNZEK · pith_short_8: M4IX4AAQ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/M4IX4AAQCFQVNZEK4NN5QNLNH5 \
  | 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: 67117e0010116156e48ae35bd8356d3f6befc912ae31a7727770a0164b37403b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cdcd4e3704537518b477bd95f084e53394106bc85e8c59dc11521c02b76a1bad",
    "cross_cats_sorted": [
      "cond-mat.mes-hall",
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2026-05-15T08:07:32Z",
    "title_canon_sha256": "185bea2800b00c51885fdf8c7859f659975b8d5ee70a9f1aaed8d49fb8fde11b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15716",
    "kind": "arxiv",
    "version": 1
  }
}