The O(infty) nonlinear sigma model out of equilibrium

Abstract

The out-of-equilibrium dynamics of the O(N+1) nonlinear sigma model in 1+1 dimensions is investigated in the large N limit. Regarding the nonlinearity as the effect of a suitable large coupling limit of the O(N+1) \phi^4 model, we first of all verify that the two limits commute, so that the O(infty) nonlinear sigma model is uniquely defined. Such model can be completely renormalized also in the out-of-equilibrium context, allowing us to study the consequences of its asymptotic freedom on the time evolution far from equilibrium. In particular we numerically study the spectrum of produced particles during the relaxation of an initial condensate and find no evidence for parametric resonance, a result that is consistent with the presence of the nonlinear contraint. Only a weak nonlinear resonance at late times is observed.