{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"ad8016e4fd4012e80d6db63a083b10965a42e5b00a2ac5cd0ebc4f045231decc","created":"2026-10-03T07:17:59Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","8753dd13b8621663d17902cb1316503429646ae2d264b03037291ba964898bf8"],"salt":"48b3059000391d4346b96050290db17aee29bd91d100e69f6ecc67d602671c21","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"cm.dqpt.equilibrium-criticality-link","kind":"well-posed","literature_status":"open","n":"1","parents":[{"note":"","parent_revision":"8753dd13b8621663d17902cb1316503429646ae2d264b03037291ba964898bf8","relation":"special_case"}],"plain":"Kinks in the return probability were first found for sudden changes that cross an ordinary phase transition. Some models show kinks without such a crossing, and others show a crossing without kinks, and the rule that decides which happens is missing.","posed_since":"","precise":"For a quench $H_i \\to H_f$ with Loschmidt rate $l(t) = -\\operatorname{lim}_{N \\to \\infty} (1/N) \\operatorname{ln} \\mid\\langle\\psi_0\\mid \\operatorname{exp}(-i H_f t/\\hbar) \\mid\\psi_0\\rangle\\mid^2$, determine the conditions on $(H_i, H_f)$ under which nonanalytic times $t_c$ exist if and only if the quench crosses an equilibrium critical point. Known counterexamples from 2014 on violate both directions in specific models. Answer: a criterion valid for interacting nonintegrable models.","problem_ref":null,"references":"","settled_by":"A criterion proved, or verified numerically across interacting nonintegrable models in $d = 1\\text{ and }2$.","status_note":"","title":"Do dynamical transitions occur only for quenches across critical 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