Anomalous time correlations in quenched systems with continuous symmetry

We continue our exploration of the growth kinetics of the time-dependent Ginsburg-Landau model after a rapid temperature quench in the limit of large N---the number of components of the order parameter. We focus here on time-displaced correlation functions and the approach to the linear-response regime where the dynamics are governed by fluctuations in equilibrium. In the case where one correlates fields at times t and t+{τ}, with the time after the quench t small, one finds, for typical values of the wave number, that the Fourier transform of the correlation function falls rather rapidly to zero for sufficiently large {τ} as the fields lose correlation. However, for q near and equal to zero this decay can be extremely slow and serves as a measure of the softness of the restoring force in the system for long times where there are well-developed Nambu-Goldstone modes. For q=0 these correlations grow with a power-law dependence on {τ} and the q=0 component is nonergodic.