{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:X5UWJ5SLBPR6VMRCNF63NIG2CS","short_pith_number":"pith:X5UWJ5SL","schema_version":"1.0","canonical_sha256":"bf6964f64b0be3eab222697db6a0da148341294ba4c19e5782500784bdd3a175","source":{"kind":"arxiv","id":"1902.04594","version":3},"attestation_state":"computed","paper":{"title":"Removing instabilities in the hierarchical equations of motion: exact and approximate projection approaches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"physics.chem-ph","authors_text":"David R. Reichman, Ian S. Dunn, Roel Tempelaar","submitted_at":"2019-02-12T19:01:42Z","abstract_excerpt":"The hierarchical equations of motion (HEOM) provide a numerically exact approach for computing the reduced dynamics of a quantum system linearly coupled to a bath. We have found that HEOM contains temperature-dependent instabilities that grow exponentially in time. In the case of continuous-bath models, these instabilities may be delayed to later times by increasing the hierarchy dimension; however, for systems coupled to discrete, non-dispersive modes, increasing the hierarchy dimension does little to alleviate the problem. We show that these instabilities can also be removed completely at a "},"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":"1902.04594","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2019-02-12T19:01:42Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"a584c537439f574c94890ad25e7619fd63001faf2646c026a4a3a2145fab9158","abstract_canon_sha256":"3d28eeb6cef8de594c8299a737f9fc6976673d376c0e1e2e2463e4acd6e06bcd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:31.906486Z","signature_b64":"7WHxnP4Q1eEakaXrX0ZSvbChDNJBpc5rcuz1UNBOiHpZQYy6CrSM3otrGjGiR0jQ/Sh2ryVcUUuTPSdyw2rbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf6964f64b0be3eab222697db6a0da148341294ba4c19e5782500784bdd3a175","last_reissued_at":"2026-05-17T23:46:31.905770Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:31.905770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Removing instabilities in the hierarchical equations of motion: exact and approximate projection approaches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"physics.chem-ph","authors_text":"David R. Reichman, Ian S. Dunn, Roel Tempelaar","submitted_at":"2019-02-12T19:01:42Z","abstract_excerpt":"The hierarchical equations of motion (HEOM) provide a numerically exact approach for computing the reduced dynamics of a quantum system linearly coupled to a bath. We have found that HEOM contains temperature-dependent instabilities that grow exponentially in time. In the case of continuous-bath models, these instabilities may be delayed to later times by increasing the hierarchy dimension; however, for systems coupled to discrete, non-dispersive modes, increasing the hierarchy dimension does little to alleviate the problem. We show that these instabilities can also be removed completely at a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04594","kind":"arxiv","version":3},"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":"1902.04594","created_at":"2026-05-17T23:46:31.905888+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.04594v3","created_at":"2026-05-17T23:46:31.905888+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.04594","created_at":"2026-05-17T23:46:31.905888+00:00"},{"alias_kind":"pith_short_12","alias_value":"X5UWJ5SLBPR6","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"X5UWJ5SLBPR6VMRC","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"X5UWJ5SL","created_at":"2026-05-18T12:33:33.725879+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/X5UWJ5SLBPR6VMRCNF63NIG2CS","json":"https://pith.science/pith/X5UWJ5SLBPR6VMRCNF63NIG2CS.json","graph_json":"https://pith.science/api/pith-number/X5UWJ5SLBPR6VMRCNF63NIG2CS/graph.json","events_json":"https://pith.science/api/pith-number/X5UWJ5SLBPR6VMRCNF63NIG2CS/events.json","paper":"https://pith.science/paper/X5UWJ5SL"},"agent_actions":{"view_html":"https://pith.science/pith/X5UWJ5SLBPR6VMRCNF63NIG2CS","download_json":"https://pith.science/pith/X5UWJ5SLBPR6VMRCNF63NIG2CS.json","view_paper":"https://pith.science/paper/X5UWJ5SL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.04594&json=true","fetch_graph":"https://pith.science/api/pith-number/X5UWJ5SLBPR6VMRCNF63NIG2CS/graph.json","fetch_events":"https://pith.science/api/pith-number/X5UWJ5SLBPR6VMRCNF63NIG2CS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X5UWJ5SLBPR6VMRCNF63NIG2CS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X5UWJ5SLBPR6VMRCNF63NIG2CS/action/storage_attestation","attest_author":"https://pith.science/pith/X5UWJ5SLBPR6VMRCNF63NIG2CS/action/author_attestation","sign_citation":"https://pith.science/pith/X5UWJ5SLBPR6VMRCNF63NIG2CS/action/citation_signature","submit_replication":"https://pith.science/pith/X5UWJ5SLBPR6VMRCNF63NIG2CS/action/replication_record"}},"created_at":"2026-05-17T23:46:31.905888+00:00","updated_at":"2026-05-17T23:46:31.905888+00:00"}