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Here $\\sigma := (\\sigma_1,\\sigma_2,\\sigma_3)$ are the $2 \\times 2$ Pauli matrices and $V$ is a hermitian potential decaying exponentially in the direction of the magnetic field $\\textbf{B} := \\text{curl} \\hspace{0.6mm} \\textbf{A}$. We give a representation of the derivative of the SSF as a sum of the imaginary part of a holomorphic function and a harmonic measure related to the resonances of $H_V$."},"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":"1506.05759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-06-18T17:53:29Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"a10a9f5491815881a4bdca4d3aba6218c165b84d6e72b657628be5b032b93de2","abstract_canon_sha256":"a65e70012489c46bf9076d3888e703c2540c4bd606d1817313a3c0177f0973bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:09.761160Z","signature_b64":"aXA7SNL/Y7fiJvV2n4s8ybmP2/blPemApetS18VUcNSfFhjPUSP1Q9RRHDRXkH8ffNiVdFcwS5WEzI2gHD8TDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"225ae13cd9507c17b2f2717c8b5b144112df205fe0e3abc70878e814a7130bd0","last_reissued_at":"2026-05-18T01:44:09.760490Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:09.760490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral shift function and Resonances near the low ground state for Pauli and Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Diomba Sambou","submitted_at":"2015-06-18T17:53:29Z","abstract_excerpt":"We study the spectral shift function (SSF) $\\xi(\\lambda)$ and the resonances of the operator $H_V := \\big( \\sigma \\cdot (-i\\nabla - \\textbf{A}) \\big)^{2} + V$ in $L^2(\\mathbb{R}^3)$ near the origin. 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