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 fo r large initial energy densities, and after linear unstabilities (para metric or spinodal) are shut off by the quantum back reaction. A new t ime scale emerges that separates the linear from the non-linear regime s. This scale is non-perturbative in the coupling and initial amplitud e. The non-perturbative evolution is studied within the context of the O(N) vector model in the large N limit. A combination of numerical an alysis and the implementation of a dynamical renormalization group res ummation via multi-time-scale analysis reveals the presence of unstabl e bands in the nonlinear regime. These are associated with power law g rowth of quantum fluctuations, that result in power law relaxation and dissipation with non-universal and non-perturbative dynamical anomalo us exponents. We find that there is substantial particle production du ring this non-linear evolution which is of the same order as that in t he linear regime and results in a non-perturbative distribution. The e xpectation value of the scalar field vanishes asymptotically transferr ing all of the initial energy into produced particles via the non-line ar resonances in the unbroken symmetry phase. The effective mass squar ed for the quantum modes tends asymptotically to a constant plus oscil lating O(1/t) terms. This slow approach to asymptotia causes the power behavior of the modes which become free harmonic modes for late enoug h time. We derive a simple expression for the equation of state for th e fluid of produced particles that interpolates between radiation-type and dust-type equations according to the initial value of the order p arameter for unbroken symmetry. For broken symmetry the produced parti cles are asymptotically massless Goldstone bosons with an ultrarelativ istic equation of state. We find the onset of a novel form of dynamica l Bose condensation in the collisionless regime in the absence of ther malization.