{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7KASKQVQ5PJ7UVVZRC463KCYAP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7d2e578493b0ac579bf9a200e9433dab219ed72cd564a1568009b19f43249cc7","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-05T16:14:56Z","title_canon_sha256":"83ee9ac468920edcfa0d8975892daf7f6110c9603ff644a7f04ef2938d24ed99"},"schema_version":"1.0","source":{"id":"1312.1600","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1600","created_at":"2026-05-18T01:45:58Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1600v1","created_at":"2026-05-18T01:45:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1600","created_at":"2026-05-18T01:45:58Z"},{"alias_kind":"pith_short_12","alias_value":"7KASKQVQ5PJ7","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7KASKQVQ5PJ7UVVZ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7KASKQVQ","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:887a3eb5c2a1e3c723c54c39d16c6908eec91096857105eb62a223539c34e544","target":"graph","created_at":"2026-05-18T01:45:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Using quantum parallelism on random walks as original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers -- with internal degrees of freedom which serve as random gyroscopes -- interacting with series of probes. These processes may also be viewed as the scaling limit of open quantum random walks and we develop this approach along three different lines: quantum trajectory, quantum dynamical map, and quantum stochastic differential equation. We also present a study of the simplest case, with a two level system as","authors_text":"Antoine Tilloy, Denis Bernard, Michel Bauer","cross_cats":["cond-mat.stat-mech","math.MP","math.PR","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-05T16:14:56Z","title":"The Open Quantum Brownian Motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1600","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:99ae6479f4961ab68ece896bd4420a1b1bc69976a9fc3296609e7f2612eccf3a","target":"record","created_at":"2026-05-18T01:45:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7d2e578493b0ac579bf9a200e9433dab219ed72cd564a1568009b19f43249cc7","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-05T16:14:56Z","title_canon_sha256":"83ee9ac468920edcfa0d8975892daf7f6110c9603ff644a7f04ef2938d24ed99"},"schema_version":"1.0","source":{"id":"1312.1600","kind":"arxiv","version":1}},"canonical_sha256":"fa812542b0ebd3fa56b988b9eda85803d172985d688d88538c8efe7a73fadcff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa812542b0ebd3fa56b988b9eda85803d172985d688d88538c8efe7a73fadcff","first_computed_at":"2026-05-18T01:45:58.251105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:45:58.251105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c4SoZ4lywIYvxuRXwJeE6e7jYIqCJIhJ2RTULap8Iq/xcCFTa6Ywbe+WtxIagnqdwqu17CZrdz3FEOSe018eBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:45:58.251595Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1600","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99ae6479f4961ab68ece896bd4420a1b1bc69976a9fc3296609e7f2612eccf3a","sha256:887a3eb5c2a1e3c723c54c39d16c6908eec91096857105eb62a223539c34e544"],"state_sha256":"cb067099f6b0e9bdfa93fdee16bab33555725039ded4f0c3dfa05a2ee5c65936"}