Asymptotic dynamics in scalar field theory: Anomalous relaxation

Abstract

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 backreaction. 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(N ) vector model in the large N limit. A combination of numerical analysis and the implementation of a dynamical renormalization group resummation via multitime 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 O(1/t) terms. This slow approach to asymptotia causes the power behaviour 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 sym- * Laboratoire Associé au CNRS UA280.

Nonequilibrium dynamics in quantum field theory at high density: The “tsunami”

“…A similar asymptotic decay has been found in this model for zero particle initial conditions and ζ(0) = 0 [9].…”

“…we have the equation of state, 9) and interpolates between a cold matter (for q 0 ≪ 1), and a radiation (for q 0 ≫ 1) equation of state. • M 2 ∞ = 0 This can only happen if α = −1 (m 2 R < 0).…”

“…This resonant effect is negligible for small λ. (Parametric unstabilities are shut off by the backreaction for no particle initial conditions [8][9][10]). …”

Renormalization of nonequilibrium dynamics at largeNand finite temperature

“…An interesting topic which has emerged recently [30] is a sum rule for the late time behaviour, which was found to be satisfied numerically with high precision. Adapted to our notation and definitions, and generalized (naively) to finite temperature, it reads…”

Dynamical renormalization group resummation of finite temperature infrared divergences

“…The main concept in this programme is the resummation of secular terms in the perturbative solution of the equation of evolution of expectation values that determine the real time retarded propagators. This dynamical renormalization group was originally developed to improve the solutions of ordinary (and partial) differential equations [37], and has been recently implemented in quantum field theory out of equilibrium [38,39] where it reveals relaxation with anomalous (and nonperturbative) exponents [39] (for other applications in quantum mechanics of few degrees of freedom see [40]). …”