{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:M47JMVMEIOBZHYKG6FREPEMXXG","short_pith_number":"pith:M47JMVME","schema_version":"1.0","canonical_sha256":"673e965584438393e146f162479197b9a83e544f7bf2ecc9499782bbb88b328b","source":{"kind":"arxiv","id":"1707.05084","version":1},"attestation_state":"computed","paper":{"title":"Analytic Theory of Wannier-Stark Quantization in Two Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Alexander Onipko, Lyuba Malysheva","submitted_at":"2017-07-17T10:39:01Z","abstract_excerpt":"For the first time, one-particle theory of Wannier-Stark quantization for a $a(N$$-$1)-long chain affected by a homogeneous electric field $E_e$ is extended to the 2D case of $L_N$=$a(N$$-$1)-long and $L_{\\cal N}$=$a$$({\\cal N}$$-$1)-wide conductor, which is modeled by the atomic square lattice with the electron site-energy change from atom to atom in the direction parallel to $\\cal N$ axis by the amount of electric field parameter (efp) $\\varepsilon \\equiv aeE_e/|t| $ in units of $|t|$. It is shown that each field-provoked $\\mu$-level in the chain spectrum gives birth to the $\\mu$-subband of "},"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":"1707.05084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2017-07-17T10:39:01Z","cross_cats_sorted":[],"title_canon_sha256":"cb6d94e588173da948a94660164305c85d53844411eb38ab848200ab4b0a8fc3","abstract_canon_sha256":"72f7178e78e48bebb73361131713e565141e6248582a1e5c9ad3fff42c69770d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:11.434287Z","signature_b64":"LZLv7uOdQg585B/qxt7bYyNY/bCkXOH2i0mOu7UKjjo0wpEPLgeXBnU1LuyfLU5O5s3t4BQocDCY9Mn2Ui31CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"673e965584438393e146f162479197b9a83e544f7bf2ecc9499782bbb88b328b","last_reissued_at":"2026-05-18T00:40:11.433847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:11.433847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic Theory of Wannier-Stark Quantization in Two Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Alexander Onipko, Lyuba Malysheva","submitted_at":"2017-07-17T10:39:01Z","abstract_excerpt":"For the first time, one-particle theory of Wannier-Stark quantization for a $a(N$$-$1)-long chain affected by a homogeneous electric field $E_e$ is extended to the 2D case of $L_N$=$a(N$$-$1)-long and $L_{\\cal N}$=$a$$({\\cal N}$$-$1)-wide conductor, which is modeled by the atomic square lattice with the electron site-energy change from atom to atom in the direction parallel to $\\cal N$ axis by the amount of electric field parameter (efp) $\\varepsilon \\equiv aeE_e/|t| $ in units of $|t|$. It is shown that each field-provoked $\\mu$-level in the chain spectrum gives birth to the $\\mu$-subband of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05084","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":"1707.05084","created_at":"2026-05-18T00:40:11.433913+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.05084v1","created_at":"2026-05-18T00:40:11.433913+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05084","created_at":"2026-05-18T00:40:11.433913+00:00"},{"alias_kind":"pith_short_12","alias_value":"M47JMVMEIOBZ","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"M47JMVMEIOBZHYKG","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"M47JMVME","created_at":"2026-05-18T12:31:28.150371+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/M47JMVMEIOBZHYKG6FREPEMXXG","json":"https://pith.science/pith/M47JMVMEIOBZHYKG6FREPEMXXG.json","graph_json":"https://pith.science/api/pith-number/M47JMVMEIOBZHYKG6FREPEMXXG/graph.json","events_json":"https://pith.science/api/pith-number/M47JMVMEIOBZHYKG6FREPEMXXG/events.json","paper":"https://pith.science/paper/M47JMVME"},"agent_actions":{"view_html":"https://pith.science/pith/M47JMVMEIOBZHYKG6FREPEMXXG","download_json":"https://pith.science/pith/M47JMVMEIOBZHYKG6FREPEMXXG.json","view_paper":"https://pith.science/paper/M47JMVME","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.05084&json=true","fetch_graph":"https://pith.science/api/pith-number/M47JMVMEIOBZHYKG6FREPEMXXG/graph.json","fetch_events":"https://pith.science/api/pith-number/M47JMVMEIOBZHYKG6FREPEMXXG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M47JMVMEIOBZHYKG6FREPEMXXG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M47JMVMEIOBZHYKG6FREPEMXXG/action/storage_attestation","attest_author":"https://pith.science/pith/M47JMVMEIOBZHYKG6FREPEMXXG/action/author_attestation","sign_citation":"https://pith.science/pith/M47JMVMEIOBZHYKG6FREPEMXXG/action/citation_signature","submit_replication":"https://pith.science/pith/M47JMVMEIOBZHYKG6FREPEMXXG/action/replication_record"}},"created_at":"2026-05-18T00:40:11.433913+00:00","updated_at":"2026-05-18T00:40:11.433913+00:00"}