Real-time relaxation and kinetics in hot scalar QED: Landau damping - art.no. 125009

The real time evolution of non-equilibrium expectation values with soft len gth scales similar to k(-1)>(eT)(-1) is solved in hot scalar electrodynamic s, with a view towards understanding relaxational phenomena in the QGP and the electroweak plasma. We find that the gauge invariant non-equilibrium ex pectation values relax via power laws to asymptotic amplitudes that are det ermined by the quasiparticle poles. The long time relaxational dynamics and relevant time scales are determined by the behavior of the retarded self-e nergy not at the small frequencies, but at the Landau damping thresholds. T his explains the presence of power laws and not of exponential decay. In th e process we rederive the Hn, effective action using non-equilibrium field theory. Furthermore we obtain the influence functional, the Langevin equati on and the fluctuation-dissipation theorem for the soft modes, identifying the correlators that emerge in the classical limit. We show that a Markovia n approximation fails to describe the dynamics both at short and long times . We find that the distribution function for soft quasiparticles relaxes wi th a power law through Landau damping. We also introduce a novel kinetic ap proach that goes beyond the standard Boltzmann equation by incorporating of f-shell processes and find that the distribution function for soft quasipar ticles relaxes with a power law through Landau damping. We find an unusual dressing dynamics of bare particles and anomalous (logarithmic) relaxation of hard quasiparticles. [S0556-2821(98)03722-9].