  Classical real-time lattice simulations play an important role in
understanding non-equilibrium phenomena in gauge theories and are used in
particular to model the prethermal evolution of heavy-ion collisions. Above the
Debye scale the classical Yang-Mills (CYM) theory can be matched smoothly to
kinetic theory. First we study the limits of the quasiparticle picture of the
CYM fields by determining the plasmon mass of the system using 3 different
methods. Then we argue that one needs a numerical calculation of a system of
classical gauge fields and small linearized fluctuations which correspond to
quantum fluctuations, in a way that keeps the separation between the two
manifest. We demonstrate and test an implementation of an algorithm with the
linearized fluctuations showing that the linearization indeed works and the
Gauss's law is conserved.
