  Understanding the out-of-equilibrium dynamics of a closed quantum system
driven across a quantum phase transition is an important problem with
widespread implications for quantum state preparation and adiabatic algorithms.
While the quantum Kibble-Zurek mechanism elucidates part of these dynamics, the
subsequent and significant coarsening processes lie beyond its scope. Here, we
develop a universal description of such coarsening dynamics -- and their
interplay with the Kibble-Zurek mechanism -- in terms of scaling theories. Our
comprehensive theoretical framework applies to a diverse set of ramp protocols
and encompasses various coarsening scenarios involving both quantum and thermal
fluctuations. Moreover, we highlight how such coarsening dynamics can be
directly studied in today's "synthetic" quantum many-body systems, including
Rydberg atom arrays, and present a detailed proposal for their experimental
observation.
