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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 $l(t) = -\\lim_{N \\to \\infty} (1/N) \\ln \\mid\\langle\\psi_0\\mid \\exp(-i H_f t/\\hbar) \\mid\\psi_0\\rangle\\mid^2$, 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":"5833294d540db64b65f4b3009f4de7c43c3d1b5d7d529061d41247e284a1df41","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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