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We study critical dynamics through time evolution of quantum \u000Cfield theories driven to a Lifshitz-
like fi\u000Cxed point, with z > 1, under relevant deformations. The deformations we consider are fast
smooth quantum quenches, namely when the quench scale \delta t
^{-z} is large compared to the deformation scale. We show that in holographic models the response of the system merely depends on the scaling
dimension of the quenched operator as \delta \lambda .\delta t^{d-2Î+z-1}, where \delta \lambda
is the deformation amplitude. This scaling behavior is enhanced logarithmically in certain cases. We also study free Lifshitz scalar
theory deformed by mass operator and show that the universal scaling of the response completely
matches with holographic analysis. We argue that this scaling behavior is universal for any relevant
deformation around Lifshitz-like UV fi\u000Cxed points.
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