  We address the quantum dynamics of a system composed of a qubit globally
coupled to a many-body system characterized by short-range interactions. We
employ a dynamic finite-size scaling framework to investigate the
out-of-equilibrium dynamics arising from the sudden variation (turning on) of
the interaction between the qubit and the many-body system, in particular when
the latter is in proximity of a quantum first-order or continuous phase
transition. Although the approach is quite general, we consider d-dimensional
quantum Ising spin models in the presence of transverse and longitudinal
fields, as paradigmatic quantum many-body systems. To characterize the
out-of-equilibrium dynamics, we focus on a number of quantum-information
oriented properties of the model. Namely, we concentrate on the decoherence
features of the qubit, the energy interchanges among the qubit and the
many-body system during the out-of-equilibrium dynamics, and the work
distribution associated with the quench. The scaling behaviors predicted by the
dynamic finite-size scaling theory are verified through extensive numerical
computations for the one-dimensional Ising model, which reveal a fast
convergence to the expected asymptotic behavior with increasing the system
size.
