Asymptotic dynamics in scalar field theory: Anomalous relaxation

We analyze the dynamics of dissipation and relaxation in the unbroken and broken symmetry phases of scalar theory in the nonlinear regime for large initial energy densities, and after linear unstabilities (parametric or spinodal) are shut off by the quantum back reaction. A new time scale emerges that separates the linear from the non-linear regimes. This scale is non-perturbative in the coupling and initial amplitude. The non-perturbative evolution is studied within the context of the $O\left(N\right)\mathrm{}$ vector model in the large $N$ limit. A combination of numerical analysis and the implementation of a dynamical renormalization group resummation via multi-time-scale analysis reveals the presence of unstable bands in the nonlinear regime. These are associated with power law growth of quantum fluctuations, that result in power law relaxation and dissipation with non-universal and non-perturbative dynamical anomalous exponents. We find that there is substantial particle production during this non-linear evolution which is of the same order as that in the linear regime and results in a non-perturbative distribution. The expectation value of the scalar field vanishes asymptotically transferring all of the initial energy into produced particles via the non-linear resonances in the unbroken symmetry phase. The effective mass squared for the quantum modes tends asymptotically to a constant plus oscillating $\mathcal{O}\mathrm{}(1/t)\mathrm{}$ terms. This slow approach to asymptotia causes the power behavior of the modes which become free harmonic modes for late enough time. We derive a simple expression for the equation of state for the fluid of produced particles that interpolates between radiation-type and dust-type equations according to the initial value of the order parameter for unbroken symmetry. For broken symmetry the produced particles are asymptotically massless Goldstone bosons with an ultrarelativistic equation of state. We find the onset of a novel form of dynamical Bose condensation in the collisionless regime in the absence of thermalization.