{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"5d45709e1c375457470f338b8fe8abd0c1f89a172c0e83878851e2573bf63141","created":"2026-10-03T07:17:59Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"59591d244d012d2cc37d7304a4ac1b85c2ef7d942d00758b24c53c841c197669","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":"1","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 $l(t) = -\\operatorname{lim}_{N \\to \\infty} (1/N) \\operatorname{ln} \\mid\\langle\\psi_0\\mid \\operatorname{exp}(-i H_f t/\\hbar) \\mid\\psi_0\\rangle\\mid^2$ 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":null,"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":"f0f2c6f7bdd6262d6700dc8806ab5f70f58e1999b1e12bad11c2bf274d3c1f12"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"8753dd13b8621663d17902cb1316503429646ae2d264b03037291ba964898bf8","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"24d31b5fa484ae190210aed81efa079c17f337c1d2c6b5ac5d6840900f3d6617","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"n4jMEtytLuyk5W7du0XGVtGxSx2u__XDABArpiByhMvGqKDx-a_wMLKrLQujZw-mCRcNiQV9O5s_ZwpQW47bAw"},"schema":"pubphys.envelope/1"},"record_hash":"8753dd13b8621663d17902cb1316503429646ae2d264b03037291ba964898bf8","leaf_index":955}