  We calculate the fluorescence spectra of a driven lattice of coupled
cavities. To do this, we extend methods of evaluating two-time correlations in
infinite lattices to open quantum systems; this allows access to momentum
resolved fluorescence spectrum. We illustrate this for a driven-dissipative
transverse field anisotropic XY model. By studying the fluctuation dissipation
theorem, we find the emergence of a quasi-thermalized steady state with a
temperature dependent on system parameters; for blue detuned driving, we show
this effective temperature is negative. In the low excitation density limit, we
compare these numerical results to analytical spin-wave theory, providing an
understanding of the form of the distribution function and the origin of
quasi-thermalization.
