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We investigate the effects of fluctuations on the dynamics of an isolatedquantum system represented by a $\phi^4$ field theory with $O(N)$ symmetryafter a quench in $d>2$ spatial dimensions. A perturbativerenormalization-group approach involving a dimensional expansion in$\epsilon=4-d$ is employed in order to study the evolution within a prethermalregime controlled by elastic dephasing. In particular, we focus on a quenchfrom a disordered initial state to the critical point, which introduces aneffective temporal boundary in the evolution. At this boundary, the relevantfields acquire an anomalous scaling dimension, while the evolution of both theorder parameter and its correlation and response functions display universalaging. Since the relevant excitations propagate ballistically, a light cone inreal space emerges. At longer times, the onset of inelastic scattering appearsas secularly growing self-generated dissipation in the effective Keldysh fieldtheory, with the strength of the dissipative vertices providing an estimate forthe time needed to leave the prethermal regime.

Short-time universal scaling and light-cone dynamics after a quench in an isolated quantum system in $d$ spatial dimensions