Role of quantum fluctuations in a system with strong fields: Spectral properties and thermalization

In a previous work [], we have studied the evolution of a scalar field with a quartic coupling, driven by a classical source that initializes it to a non-perturbatively large value. At leading order in the coupling, the evolution of this system is given by classical solutions of the field equation of motion. However, this system is subject to a parametric resonance that leads to secular divergences in higher-order corrections to physical observables. We have proposed a scheme that resums all the leading secular terms: this resummation leads to finite results at all times, and we have observed also that it makes the pressure tensor of the system relax to its equilibrium value. In the present paper, we continue the study of this system by looking at finer details of its dynamics. We first compute its spectral function at various stages of the evolution, and we observe that after a fairly short transient time there are well-defined massive quasi-particles. We then consider the time evolution of the momentum distribution of these quasi-particles, and we show that after a stage dominated by the parametric resonance, this distribution slowly evolves to an equilibrium distribution. Interestingly, this distribution develops a transient chemical potential, signaling the fact that number changing processes are much slower than the elastic ones.