  We study the critical behavior of the nonequilibrium dynamics and of the
steady states emerging from the competition between coherent and dissipative
dynamics close to quantum phase transitions. The latter is induced by the
coupling of the system with a Markovian bath, such that the evolution of the
system's density matrix can be effectively described by a Lindblad master
equation. We devise general scaling behaviors for the out-of-equilibrium
evolution and the stationary states emerging in the large-time limit for
generic initial conditions, in terms of the parameters of the Hamiltonian
providing the coherent driving and those associated with the dissipative
interactions with the environment. Our framework is supported by numerical
results for the dynamics of a one-dimensional lattice fermion gas undergoing a
quantum Ising transition, in the presence of dissipative mechanisms which
include local pumping and decay of particles.
