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The vector potential has the form $A=c_0\\bigg(\\frac{-y}{{x^2+y^2}}; \\frac{x}{{x^2+y^2}} \\bigg)+ \\frac{B}{2}\\bigg(-y; x\\bigg) $; $B>0,$ $c_0\\in]0;1[$. The asymptotics of negative eigenvalues of $H_{c_0,B,\\beta}$ for $\\beta \\longrightarrow +\\infty$ is found. We also prove that for large enough positive value of $\\beta$ the system exhibits persistent currents."},"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":"math-ph/0310055","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2003-10-25T17:16:52Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"904bc4b8e7aef42e388b5257090a6b79f93cf992148fb49b6a1193a8e875a44d","abstract_canon_sha256":"83228549aec62e2e11827df5ff68a94816cdb792e0f29cf1abfde6fcdb12957f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:31.756575Z","signature_b64":"ge1TIaY7Fo0ynwxjWOcjHBin2xK3Xz+0GakwpnhdecKBIpTAnVgU9wxFRWRRqG/oWwbZ65g0VQmtVk4LIyI+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d977f35d1adb7fe3457f5804a289ef050591d2fb7f5e0fff1c869e99bd809381","last_reissued_at":"2026-05-18T01:05:31.756011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:31.756011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics of eigenvalues of the operator describing Aharonov-Bohm effect combined with homogeneous magneticfield coupled with a strong $\\delta$-interaction on a loop","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"G.Honnouvo, M.N. Hounkonnou","submitted_at":"2003-10-25T17:16:52Z","abstract_excerpt":"We investigate the two-dimensional magnetic operator\n $H_{c_0,B,\\beta} = {(-i\\nabla -A)}^{2}-\\beta\\delta(.-\\Gamma),$ where $\\Gamma$ is a smooth loop. The vector potential has the form $A=c_0\\bigg(\\frac{-y}{{x^2+y^2}}; \\frac{x}{{x^2+y^2}} \\bigg)+ \\frac{B}{2}\\bigg(-y; x\\bigg) $; $B>0,$ $c_0\\in]0;1[$. The asymptotics of negative eigenvalues of $H_{c_0,B,\\beta}$ for $\\beta \\longrightarrow +\\infty$ is found. We also prove that for large enough positive value of $\\beta$ the system exhibits persistent currents."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0310055","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0310055","created_at":"2026-05-18T01:05:31.756101+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0310055v1","created_at":"2026-05-18T01:05:31.756101+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0310055","created_at":"2026-05-18T01:05:31.756101+00:00"},{"alias_kind":"pith_short_12","alias_value":"3F37GXI23N76","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_16","alias_value":"3F37GXI23N76GRL7","created_at":"2026-05-18T12:25:51.375804+00:00"},{"alias_kind":"pith_short_8","alias_value":"3F37GXI2","created_at":"2026-05-18T12:25:51.375804+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3F37GXI23N76GRL7LACKFCPPAU","json":"https://pith.science/pith/3F37GXI23N76GRL7LACKFCPPAU.json","graph_json":"https://pith.science/api/pith-number/3F37GXI23N76GRL7LACKFCPPAU/graph.json","events_json":"https://pith.science/api/pith-number/3F37GXI23N76GRL7LACKFCPPAU/events.json","paper":"https://pith.science/paper/3F37GXI2"},"agent_actions":{"view_html":"https://pith.science/pith/3F37GXI23N76GRL7LACKFCPPAU","download_json":"https://pith.science/pith/3F37GXI23N76GRL7LACKFCPPAU.json","view_paper":"https://pith.science/paper/3F37GXI2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0310055&json=true","fetch_graph":"https://pith.science/api/pith-number/3F37GXI23N76GRL7LACKFCPPAU/graph.json","fetch_events":"https://pith.science/api/pith-number/3F37GXI23N76GRL7LACKFCPPAU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3F37GXI23N76GRL7LACKFCPPAU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3F37GXI23N76GRL7LACKFCPPAU/action/storage_attestation","attest_author":"https://pith.science/pith/3F37GXI23N76GRL7LACKFCPPAU/action/author_attestation","sign_citation":"https://pith.science/pith/3F37GXI23N76GRL7LACKFCPPAU/action/citation_signature","submit_replication":"https://pith.science/pith/3F37GXI23N76GRL7LACKFCPPAU/action/replication_record"}},"created_at":"2026-05-18T01:05:31.756101+00:00","updated_at":"2026-05-18T01:05:31.756101+00:00"}