{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"b29ea6dd71016362dca9c5b41297dbc46fda6bf2b0b7a23ecaede3156d7afe14","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["87f7e266632f141adbf5c880f837f8a248c6bb467763ba032406e872a9e66853","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"e742f4ba4a4c0c2b815a2b9bf496eae1a065db6e76db5f731fd4a3815e67bb6a","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"cm.eth.golden-rule-scaling","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"Simple theory says a weak perturbation of strength g makes a solvable system relax at a rate proportional to g squared. The question is whether this holds exactly for very large systems or whether the rate is parametrically smaller.","posed_since":"","precise":"For $H = H_{\\mathrm{XXZ}} + g V$ with $V$ a generic local integrability-breaking perturbation not of the weak-integrability-breaking type (for that type the rate scales as $g^4$, Surace and Motrunich 2023), at infinite temperature, compute the exponent a in $\\Gamma(g) \\sim g^a$ for the decay rate of the slowest quasi-conserved local current, with $L \\to \\infty$ taken before $g \\to 0$. The golden-rule expectation is $a = 2$. Answer: the value of a, with evidence that finite-size effects are controlled (they dominate when the golden-rule rate is below the inverse traversal time of the system, or for $g$ below the size-dependent chaos threshold).","problem_ref":"87f7e266632f141adbf5c880f837f8a248c6bb467763ba032406e872a9e66853","references":"","settled_by":"An infinite-system computation of $\\Gamma(g)$ (memory-matrix or recursion-method continued fraction) agreeing with real-time numerics on systems longer than the decay length at the smallest $g$ studied.","status_note":"$g^{4}$ scaling is established for weak-integrability-breaking perturbations (Surace and Motrunich 2023; Vanovac, Surace, Motrunich 2024); the generic case is open.","title":"Does the relaxation rate scale as $g^{2}$ in the thermodynamic 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