Real-time Relaxation of Condensates 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. We rederive the HTL effective action using the techniques of non-equilibrium field theory for small amplitude condensates. We find that transverse gauge invariant condensates relax as 1/t2 and longitudinal condensates associated with plasmon (charge density) excitations relax with 1/[t log t] behavior to asymptotic amplitudes that are determined by the quasiparticle poles. The relaxational dynamics and relevant time scales are determined by the global analytic structure of the retarded propagators. To leading order, the long-time behaviour is determined by the Landau discontinuities associated with off-shell processes. Landau damping follows from the contribution of such discontinuities. We derive the influence functional for the soft (gauge invariant) degrees of freedom by integrating out the hard scales in the HTL approximation and obtain consistently the Langevin equation, the relevant fluctuation-dissipation relation and identify the correlation functions that emerge in the classical limit. We point out that both the dissipative and noise kernels are long-ranged and a Markovian approximation fails to describe the dynamics both at short and long times. A novel kinetic approach is introduced that goes beyond the standard Boltzmann equation and incorporates off-shell processes in the description of relaxation of the distribution function. We 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.