  After a quantum phase transition the quantum vacuum can break up to form
classical topological defects. We examine this process for scalar field models
with $Z_2$ symmetry for different quench rates for the phase transition. We
find that the number density of kinks at late times universally scales as $C
m^{1/2} t^{-1/2}$ where $m$ is a mass scale in the model and $C\approx 0.22$;
it does not depend on the quench timescale in contrast to the Kibble-Zurek
scaling for thermal phase transitions. A subleading correction $\propto
t^{-3/2}$ to the kink density depends on the details of the phase transition.
