  We present a new method to obtain spectral properties of a non-Abelian gauge
theory in the region where occupation numbers are high. The method to measure
the (single-particle) spectral function is based on linear response theory and
classical-statistical lattice simulations. Although we apply it to a system far
from equilibrium in a self-similar regime, the extracted spectral function can
be understood within the hard thermal loop (HTL) formalism and can thus be
connected to thermal equilibrium at high temperatures. This allows us to obtain
quantities like the lifetime of quasiparticles that are beyond the leading
order and difficult to compute within HTL. The approach has the potential to
measure transport coefficients, to study the earliest stages of heavy-ion
collisions in a controlled way and it can be employed beyond the range of
validity of HTL.
