Non-equilibrium quantum plasmas in scalar QED: photon production, magnetic and Debye masses, and conductivity

Abstract

We study the generation of a non-equilibrium plasma in scalar QED with N charged scalar fields through spinodal instabilities in the case of a super cooled second order phase transition and parametric amplification when the order parameter oscillates with large amplitude around the minimum of the potential.The focus is to study the non-equilibrium electromagnetic properties of the plasma, such as photon production, electric and magnetic screening and conductivity. A novel kinetic equation is introduced to compute photon production far away from equilibrium in the large N limit and lowest order in the electromagnetic coupling.During the early stages of the dynamics the photon density grows exponentially and asymptotically the amplitude and frequency distribution becomes \sim alpha m^2/[lambda^2 ω^3] with lambda the scalar self-coupling and m the scalar mass.In the case of a phase transition,electric and magnetic fields are correlated on distances xi(t) \sim sqrt{t} during the early stages and the power spectrum is peaked at low momentum. Magnetic and Debye screening masses are defined out of equilibrium. The magnetic mass vanishes out of equilibrium in this abelian models. The Debye mass turns to be m^2_{Deb} \sim alpha m^2/lambda for a supercooled phase transition while in the case of an oscillating order parameter an interpolating time dependent Debye mass grows as alpha sqrt{m t}/lambda due to a non-linear resonance at low momentum in the charged particle distribution. The build-up of the transverse electric conductivity is studied during the formation of the non-equilibrium plasma. Its long wavelength limit reaches a value sigma_{k\approx 0} \sim alpha m/lambda at the end of the stage of linear instabilities. Its asymptotic form in terms of the non-equilibrium particle distribution functions is derived.