We analyze the phenomenon of preheating, i.e., explosive particle production due to parametric amplification of quantum fluctuations in the unbroken symmetry case, or spinodal instabilities in the broken symmetry phase, using the Minkowski space O(N) vector model in the large N limit to study the nonperturbative issues involved. We give analytic results for weak couplings and times short compared to the time at which the fluctuations become of the same order as the tree level terms, as well as numerical results including the full back reaction. In the case where the symmetry is unbroken, the analytical results agree spectacularly well with the numerical ones in their common domain of validity. In the broken symmetry case, interesting situations, corresponding to slow roll initial conditions from the unstable minimum at the origin, give rise to a new and unexpected phenomenon: the dynamical relaxation of the vacuum energy. That is, particles are abundantly produced at the expense of the quantum vacuum energy while the zero mode comes back to almost its initial value. In both cases we obtain analytically and numerically the equation of state which in both cases can be written in terms of an effective polytropic index that interpolates between vacuum and radiationlike domination. We find that simplified analyses based on the harmonic behavior of the zero mode, giving rise to a Mathieu equation for the nonzero modes, miss important physics. Furthermore, such analyses that do not include the full back reaction and do not conserve energy result in unbound particle production. Our results rule out the possibility of symmetry restoration by nonequilibrium fluctuations in the cases relevant for new inflationary scenarios. Finally, estimates of the reheating temperature are given, as well as a discussion of the inconsistency of a kinetic approach to thermalization when a nonperturbatively large number of particles are created. ͓S0556-2821͑96͒05524-5͔

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.