  We study the spectral properties of a highly occupied non-Abelian
non-equilibrium plasma appearing ubiquitously in weak coupling descriptions of
QCD matter. The spectral function of this far-from-equilibrium plasma is
measured by employing linear response theory in classical-statistical real-time
lattice Yang-Mills simulations. We establish the existence of transversely and
longitudinally polarized quasiparticles and obtain their dispersion relations,
effective mass, plasmon frequency, damping rate and further structures in the
spectral and statistical functions. Our new method can be interpreted as a
non-perturbative generalization of hard thermal loop (HTL) effective theory. We
see indications that our results approach leading order HTL in the appropriate
limit. The method can also be employed beyond the range of validity of HTL.
