{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2000:UBDRVBQE2HHROVNSCGZBMTE5GO","short_pith_number":"pith:UBDRVBQE","schema_version":"1.0","canonical_sha256":"a0471a8604d1cf1755b211b2164c9d33a98ba964b1762fc6a030b4582e349744","source":{"kind":"arxiv","id":"physics/0011010","version":1},"attestation_state":"computed","paper":{"title":"Diffusion Effects on the Breakdown of a Linear Amplifier Model Driven by the Square of a Gaussian Field","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.plasm-ph","authors_text":"A. Asselah, J. L. Lebowitz, P. Dai Pra, Ph. Mounaix","submitted_at":"2000-11-03T18:31:56Z","abstract_excerpt":"We investigate solutions to the equation $\\partial_t{\\cal E} - {\\cal D}\\Delta {\\cal E} = \\lambda S^2{\\cal E}$, where $S(x,t)$ is a Gaussian stochastic field with covariance $C(x-x',t,t')$, and $x\\in {\\mathbb R}^d$. It is shown that the coupling $\\lambda_{cN}(t)$ at which the $N$-th moment $<{\\cal E}^N(x,t)>$ diverges at time $t$, is always less or equal for ${\\cal D}>0$ than for ${\\cal D}=0$. Equality holds under some reasonable assumptions on $C$ and, in this case, $\\lambda_{cN}(t)=N\\lambda_c(t)$ where $\\lambda_c(t)$ is the value of $\\lambda$ at which $<\\exp\\lbrack \\lambda\\int_0^tS^2(0,s)ds\\r"},"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":"physics/0011010","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"physics.plasm-ph","submitted_at":"2000-11-03T18:31:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"17f7c2870c3bea3818987b8ed29c0d5925d457f1a6ba14e072a6ee39a2d955cf","abstract_canon_sha256":"47d89b0f1d02ebbe8846fa9da717d88dd7aab7024fefcc7c16fa31bf013f1284"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:11.341895Z","signature_b64":"kulceC71VAWhfjW7pmLwCAkDFCaSRM7H9tbF81X7OgIPjSl63Lm+3dHnLrewhL/jru8zvqOa70NzCfYB9cz7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0471a8604d1cf1755b211b2164c9d33a98ba964b1762fc6a030b4582e349744","last_reissued_at":"2026-05-18T01:38:11.341228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:11.341228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Diffusion Effects on the Breakdown of a Linear Amplifier Model Driven by the Square of a Gaussian Field","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.plasm-ph","authors_text":"A. Asselah, J. L. Lebowitz, P. Dai Pra, Ph. Mounaix","submitted_at":"2000-11-03T18:31:56Z","abstract_excerpt":"We investigate solutions to the equation $\\partial_t{\\cal E} - {\\cal D}\\Delta {\\cal E} = \\lambda S^2{\\cal E}$, where $S(x,t)$ is a Gaussian stochastic field with covariance $C(x-x',t,t')$, and $x\\in {\\mathbb R}^d$. It is shown that the coupling $\\lambda_{cN}(t)$ at which the $N$-th moment $<{\\cal E}^N(x,t)>$ diverges at time $t$, is always less or equal for ${\\cal D}>0$ than for ${\\cal D}=0$. Equality holds under some reasonable assumptions on $C$ and, in this case, $\\lambda_{cN}(t)=N\\lambda_c(t)$ where $\\lambda_c(t)$ is the value of $\\lambda$ at which $<\\exp\\lbrack \\lambda\\int_0^tS^2(0,s)ds\\r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0011010","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":"physics/0011010","created_at":"2026-05-18T01:38:11.341347+00:00"},{"alias_kind":"arxiv_version","alias_value":"physics/0011010v1","created_at":"2026-05-18T01:38:11.341347+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0011010","created_at":"2026-05-18T01:38:11.341347+00:00"},{"alias_kind":"pith_short_12","alias_value":"UBDRVBQE2HHR","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_16","alias_value":"UBDRVBQE2HHROVNS","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_8","alias_value":"UBDRVBQE","created_at":"2026-05-18T12:25:50.254431+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/UBDRVBQE2HHROVNSCGZBMTE5GO","json":"https://pith.science/pith/UBDRVBQE2HHROVNSCGZBMTE5GO.json","graph_json":"https://pith.science/api/pith-number/UBDRVBQE2HHROVNSCGZBMTE5GO/graph.json","events_json":"https://pith.science/api/pith-number/UBDRVBQE2HHROVNSCGZBMTE5GO/events.json","paper":"https://pith.science/paper/UBDRVBQE"},"agent_actions":{"view_html":"https://pith.science/pith/UBDRVBQE2HHROVNSCGZBMTE5GO","download_json":"https://pith.science/pith/UBDRVBQE2HHROVNSCGZBMTE5GO.json","view_paper":"https://pith.science/paper/UBDRVBQE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=physics/0011010&json=true","fetch_graph":"https://pith.science/api/pith-number/UBDRVBQE2HHROVNSCGZBMTE5GO/graph.json","fetch_events":"https://pith.science/api/pith-number/UBDRVBQE2HHROVNSCGZBMTE5GO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UBDRVBQE2HHROVNSCGZBMTE5GO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UBDRVBQE2HHROVNSCGZBMTE5GO/action/storage_attestation","attest_author":"https://pith.science/pith/UBDRVBQE2HHROVNSCGZBMTE5GO/action/author_attestation","sign_citation":"https://pith.science/pith/UBDRVBQE2HHROVNSCGZBMTE5GO/action/citation_signature","submit_replication":"https://pith.science/pith/UBDRVBQE2HHROVNSCGZBMTE5GO/action/replication_record"}},"created_at":"2026-05-18T01:38:11.341347+00:00","updated_at":"2026-05-18T01:38:11.341347+00:00"}