{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"c1b7d814823760609c261b2552bbc96dc2d77e333935e88961262034de766bc5","created":"2026-10-03T07:17:59Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","a7060de5bf7805478da1cca6042c6f103bd2642ff9d6d3738d9b00ba74b4c273"],"salt":"6ae390b47bc67e150d00cf3df323e42fe9c99e14534280a97fdc042c13c7effb","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":"1","parents":[{"note":"","parent_revision":"a7060de5bf7805478da1cca6042c6f103bd2642ff9d6d3738d9b00ba74b4c273","relation":"special_case"}],"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":null,"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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