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 to a final one . At every time there exists a critical value of the variance s of the order parameter per degree of freedom such that the fluctuations with 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 , 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 , induces a slow non-equilibrium dynamics resembling that of systems quenched across a phase transition. (nesmcq18)