{"paper":{"title":"Nonlocal Optical Response and Surface Susceptibilities: A Systematic Derivation via Spatial Moment Expansion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Nonlocal optical response at curved interfaces condenses into a single surface susceptibility scalar at leading order.","cross_cats":["cond-mat.mes-hall","math-ph","math.MP"],"primary_cat":"physics.optics","authors_text":"Fr\\'ed\\'eric Zolla","submitted_at":"2026-05-15T08:07:32Z","abstract_excerpt":"We present a systematic theory connecting the nonlocal response kernel of a homogeneous medium to its effective surface susceptibilities for an arbitrary curved interface. 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 $\\chi^s$, equal for the tangential and normal components of the electric field. These quantities provide a constructive generalization o"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Nonlocal optical response at curved interfaces condenses into a single surface susceptibility scalar at leading order.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"814e4406c392152285736c8d1c5ffdf675fc661ca3a3831303a487979e6ebc9f"},"source":{"id":"2605.15716","kind":"arxiv","version":1},"verdict":{"id":"278ac7c0-7c5d-49d7-859d-1c15e70a01a4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:33:20.783539Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"Nonlocal optical response at curved interfaces condenses into a single surface susceptibility scalar at leading order."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15716/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T20:01:19.210968Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:41:02.770091Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:33:26.970610Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:56.013961Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"b7eb2e07a34edb9a8f2a256b9d9f8b9aefbdb4892442bd4b954ae1bee38f83f2"},"references":{"count":2,"sample":[{"doi":"10.1017/cbo9781139644181","year":1999,"title":"Electronic excitations: density-functional versus many-body green’s-function approaches","work_id":"ea3da009-30ec-4a7f-91d5-117c64548e74","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/978-3-0348-7966-8","year":2004,"title":"On the vibrations of the electronic plasma","work_id":"5f845525-2449-4f92-ac78-a7dca49daaac","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":2,"snapshot_sha256":"0b0c046901db4ddb9a892c7fe7169dc11754d76b6601f6893573b6cdbc93f1bc","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"edea9e5ff7af4670c0f4472c7a60bf3da09c31f47043e583f1b17fbfd4dbc80a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}