{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"44b7cd229954a42f1c7b5a1e4223c0333de900d8336ea5c14b461748d67debb2","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["8753dd13b8621663d17902cb1316503429646ae2d264b03037291ba964898bf8","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"2910be1733d5622842ce9f3d2bb273e593afb281d799e879675e175800660ab1","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"cm.dqpt.order-parameter-connection","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"The kinks in the return probability were first linked to crossing an ordinary phase transition, but counterexamples exist in both directions. A general rule for when they match is missing.","posed_since":"2013","precise":"For a quench $H_i \\to H_f$, the Loschmidt rate $l(t) = -\\lim_{N \\to \\infty} (1/N) \\ln \\mid\\langle\\psi_0\\mid \\exp(-i H_f t/\\hbar) \\mid\\psi_0\\rangle\\mid^2$ can be nonanalytic at critical times $t_c$. Determine conditions on $(H_i, H_f)$ under which (a) such $t_c$ exist if and only if the quench crosses an equilibrium critical point and (b) $t_c$ coincide with zeros or sign changes of the order parameter. Answer: a classification valid beyond free-fermion models.","problem_ref":"8753dd13b8621663d17902cb1316503429646ae2d264b03037291ba964898bf8","references":"","settled_by":"A general criterion proved or verified across interacting nonintegrable models in $d = 1 \\text{ and } 2$.","status_note":"Counterexamples in both directions are known since 2014; no general criterion exists.","title":"When dynamical transitions coincide with equilibrium criticality or order","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"59d2042f15c7996916c3408f90f6030060f2bc98ccae7a252a7e43a6d0474cfb","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"2a261aeef29553ea440ea98b8e472f917cc93f76b3d8186d4d2a87cd1fe7ddf9","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"XoxacFmw7hxQbuiMgGC0fG7FwWEAq8WwIVuyehjj1YnFWFu9vRBQzVqEmNM2P_YkW3a83t_nXgkK2c0anxP9BQ"},"schema":"pubphys.envelope/1"},"record_hash":"59d2042f15c7996916c3408f90f6030060f2bc98ccae7a252a7e43a6d0474cfb","leaf_index":2764}