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Nonequilibrium evolution in scalar O(N) models with spontaneous symmetry breaking

We consider the out-of-equilibrium evolution of a classical condensate field and its quantum fluctuations for a scalar O(N) model with spontaneously broken symmetry. In contrast to previous studies we do not consider the large N limit, but the case of finite N, including N=1, i.e., plain $λϕ^ 4$ theory. The instabilities encountered in the one-loop approximation are prevented, as in the large-N limit, by back reaction of the fluctuations on themselves, or, equivalently, by including a resummation of bubble diagrams. For this resummation and its renormalization we use formulations developed recently based on the effective action formalism of Cornwall, Jackiw and Tomboulis. The formulation of renormalized equations for finite N derived here represents a useful tool for simulations with realistic models. Here we concentrate on the phase structure of such models. We observe the transition between the spontaneously broken and the symmetric phase at low and high energy densities, respectively. This shows that the typical structures expected in thermal equilibrium are encountered in nonequilibrium dynamics even at early times, i.e., before an efficient rescattering can lead to thermalization.