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While this approximation is asymptotically exact at vanishing separations, quantifying corrections to PFA has been notoriously difficult. Here we use a derivative expansion to compute the leading curvature correction to PFA for metals (gold) and insulators (SiO$_2$) at room temperature. We derive an explicit expression for the amplitude $\\hat\\theta_1$ of the PFA correction to t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1112.1366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-12-06T18:14:33Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"b8f400072ec048bcb3c1f3b373d53b574c5cd8e6dfddf19b0e4edf790ee3dde1","abstract_canon_sha256":"cd07b31e377b6595e86c8a1d1b0ce5afbcad65039aa627c07767cd2e43f37bc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:16.304405Z","signature_b64":"Rd5xmstQMLNMKPt7/P5wljJQkU1VcjtpynWlU2ukYnZpJ7yqKX5wHyhIvyDRlkiYdywrl7EhEnwaynB2JL3VAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7e02b8597b0ed9007c36d72b6e9ac7c1cbd50be3649770597adc9613bed679c","last_reissued_at":"2026-05-18T01:59:16.303642Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:16.303642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Material dependence of Casimir forces: gradient expansion beyond proximity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"quant-ph","authors_text":"G. Bimonte, M. Kardar, T. Emig","submitted_at":"2011-12-06T18:14:33Z","abstract_excerpt":"A widely used method for estimating Casimir interactions [H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)] between gently curved material surfaces at short distances is the proximity force approximation (PFA). While this approximation is asymptotically exact at vanishing separations, quantifying corrections to PFA has been notoriously difficult. Here we use a derivative expansion to compute the leading curvature correction to PFA for metals (gold) and insulators (SiO$_2$) at room temperature. 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