  Motivated by the early-time dynamics of the quark-gluon plasma in high-energy
heavy-ion collisions, we extract gluonic spectral functions of overoccupied
gauge theories far from equilibrium using classical-statistical lattice
simulations and linear response theory. In 3+1 dimensions we find that the
spectral function exhibits quasiparticle excitations at all momenta that are
mostly consistent with perturbative hard-thermal loop predictions, while
partially showing nonperturbative deviations. In contrast, the structure of
excitations in 2+1 dimensions is nontrivial and nonperturbative. These
nonperturbative interactions lead to broad excitation peaks in the spectral
function, demonstrating the absence of soft quasiparticles in these theories.
This also suggests that there may be significant nonperturbative corrections
present in systems with large momentum anisotropy, which are relevant to
phenomenological applications in heavy-ion collisions.
