Real-time Relaxation and Kinetics in Hot Scalar QED: Landau Damping

The real time evolution of field condensates with soft length scales k^{-1}>(eT)^{-1} is solved in hot scalar electrodynamics, with a view towards understanding relaxational phenomena in the QGP and the electroweak plasma. We find that transverse gauge invariant non-equilibrium expectation values of fields relax via {\em power laws} to asymptotic amplitudes that are determined by the quasiparticle poles. The long time relaxational dynamics and relevant time scales are determined by the behaviour of the retarded self-energy not at the small frequencies, but at the Landau damping thresholds. This explains the presence of power laws and not of exponential decay. Furthermore, we derive the influence functional, the Langevin equation and the fluctuation-dissipation theorem for the soft modes, identifying the correlation functions that emerge in the classical limit. We show that a Markovian approximation fails to describe the dynamics {\em both} at short and long times. We also introduce a novel kinetic approach that goes beyond the standard Boltzmann equation and incorporates off-shell processes and find that the distribution function for soft quasiparticles relaxes with a power law through Landau damping. We also find an unusual dressing dynamics of bare particles and anomalous (logarithmic) relaxation of hard quasiparticles.