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The non-equilibrium dynamics of an isolated quantum system after a suddenquench to a dynamical critical point is expected to be characterized by scalingand universal exponents due to the absence of time scales. We explore thesefeatures for a quench of the parameters of a Hamiltonian with $O(N)$ symmetry,starting from a ground state in the disordered phase. In the limit of infinite$N$, the exponents and scaling forms of the relevant two-time correlationfunctions can be calculated exactly. Our analytical predictions are confirmedby the numerical solution of the corresponding equations. Moreover, we findthat the same scaling functions, yet with different exponents, also describethe coarsening dynamics for quenches below the dynamical critical point.

Aging and coarsening in isolated quantum systems after a quench: exact results for the quantum $O(N)$ model with $N \to \infty$