Dynamics of fluctuations in the Gaussian model with conserved dynamics

We study the fluctuations of the Gaussian model, with conservation of the order parameter, evolving in contact with a thermal bath quenched from an initial inverse temperature eta_i to a final one eta_f. At every time there exists a critical value s_c(t) of the variance s of the order parameter per degree of freedom such that the fluctuations with s > s_c(t) are characterized by a macroscopic contribution of the zero wavevector mode, similarly to what occurs in an ordinary condensation transition. We show that the probability of fluctuations with s < inf_t[s_c(t)], for which condensation never occurs, rapidly converges towards a stationary behavior. By contrast, the process of populating the zero wavevector mode of the variance, which takes place for s > inf_t[s_c(t)], induces a slow non-equilibrium dynamics resembling that of systems quenched across a phase transition.