  We identify significant quantum many-body effects, robust to position
fluctuations and strong dipole--dipole interactions, in the forward light
scattering from planar arrays and uniform-density disks of cold atoms, by
comparing stochastic electrodynamics simulations of a quantum master equation
and of a semiclassical model that neglects quantum fluctuations. Quantum
effects are pronounced at high atomic densities, light close to saturation
intensity, and around subradiant resonances. We show that such conditions also
maximize spin--spin correlations and entanglement of formation for the atoms,
revealing the microscopic origin of light-induced quantum effects. In several
regimes of interest, an enhanced semiclassical model with a single-atom quantum
description reproduces light transmission remarkably well, and permits analysis
of otherwise numerically inaccessible large ensembles, in which we observe
collective many-body analogues of resonance power broadening, vacuum Rabi
splitting, and significant suppression in cooperative reflection from atomic
arrays.
