{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:2PXDYWR6YJQFO22SMDNDBADTKJ","short_pith_number":"pith:2PXDYWR6","schema_version":"1.0","canonical_sha256":"d3ee3c5a3ec260576b5260da308073524e2daafb095f5c7a3fab6e5a48cdec93","source":{"kind":"arxiv","id":"1302.5459","version":1},"attestation_state":"computed","paper":{"title":"Time-Dependent Gaussian Solution for the Kostin Equation around Classical Trajectories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"A. B. Nassar, D. G. da Silva, F. Haas, J. M. F. Bassalo, M. Cattani","submitted_at":"2013-02-22T00:46:03Z","abstract_excerpt":"The structure of time-dependent Gaussian solutions for the Kostin equation in dissipative quantum mechanics is analyzed. Expanding the generic external potential near the center of mass of the wave packet, one conclude that: the center of mass follows the dynamics of a classical particle under the external potential and a damping proportional to the velocity; the width of the wave packet satisfy a non-conservative Pinney equation. An appropriate perturbation theory is developed for the free particle case, solving the long standing problem of finding analytic expressions for square integrable s"},"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":"1302.5459","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-22T00:46:03Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f77005f741bbe57ac3cec4acf2c82d6997cb96931a6fb7d1fc8dd8f931cdc020","abstract_canon_sha256":"c6419903d0c32156a38cb02dc52d08774b68d625ff489f17c241950bb7b6b591"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:51:34.254158Z","signature_b64":"C9uMkMsLjQp8vMky7cSVetxsNzdqanUpm2HQ2JKAnLe6bznonN43wPTjRgP5zI0jAG2kFuy2rMcQVL5Sef/mBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3ee3c5a3ec260576b5260da308073524e2daafb095f5c7a3fab6e5a48cdec93","last_reissued_at":"2026-05-18T01:51:34.253689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:51:34.253689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Time-Dependent Gaussian Solution for the Kostin Equation around Classical Trajectories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"A. B. Nassar, D. G. da Silva, F. Haas, J. M. F. Bassalo, M. Cattani","submitted_at":"2013-02-22T00:46:03Z","abstract_excerpt":"The structure of time-dependent Gaussian solutions for the Kostin equation in dissipative quantum mechanics is analyzed. Expanding the generic external potential near the center of mass of the wave packet, one conclude that: the center of mass follows the dynamics of a classical particle under the external potential and a damping proportional to the velocity; the width of the wave packet satisfy a non-conservative Pinney equation. An appropriate perturbation theory is developed for the free particle case, solving the long standing problem of finding analytic expressions for square integrable s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5459","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":"1302.5459","created_at":"2026-05-18T01:51:34.253762+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.5459v1","created_at":"2026-05-18T01:51:34.253762+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5459","created_at":"2026-05-18T01:51:34.253762+00:00"},{"alias_kind":"pith_short_12","alias_value":"2PXDYWR6YJQF","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"2PXDYWR6YJQFO22S","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"2PXDYWR6","created_at":"2026-05-18T12:27:32.513160+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/2PXDYWR6YJQFO22SMDNDBADTKJ","json":"https://pith.science/pith/2PXDYWR6YJQFO22SMDNDBADTKJ.json","graph_json":"https://pith.science/api/pith-number/2PXDYWR6YJQFO22SMDNDBADTKJ/graph.json","events_json":"https://pith.science/api/pith-number/2PXDYWR6YJQFO22SMDNDBADTKJ/events.json","paper":"https://pith.science/paper/2PXDYWR6"},"agent_actions":{"view_html":"https://pith.science/pith/2PXDYWR6YJQFO22SMDNDBADTKJ","download_json":"https://pith.science/pith/2PXDYWR6YJQFO22SMDNDBADTKJ.json","view_paper":"https://pith.science/paper/2PXDYWR6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.5459&json=true","fetch_graph":"https://pith.science/api/pith-number/2PXDYWR6YJQFO22SMDNDBADTKJ/graph.json","fetch_events":"https://pith.science/api/pith-number/2PXDYWR6YJQFO22SMDNDBADTKJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2PXDYWR6YJQFO22SMDNDBADTKJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2PXDYWR6YJQFO22SMDNDBADTKJ/action/storage_attestation","attest_author":"https://pith.science/pith/2PXDYWR6YJQFO22SMDNDBADTKJ/action/author_attestation","sign_citation":"https://pith.science/pith/2PXDYWR6YJQFO22SMDNDBADTKJ/action/citation_signature","submit_replication":"https://pith.science/pith/2PXDYWR6YJQFO22SMDNDBADTKJ/action/replication_record"}},"created_at":"2026-05-18T01:51:34.253762+00:00","updated_at":"2026-05-18T01:51:34.253762+00:00"}