Dynamics of fluctuations in the Gaussian model with conserved dynamics

Abstract

We study the fluctuations of the Gaussian model, with conservation of the order parameter, evolving in contact with a thermal bath quenched from inverse temperature ${\beta }_i$ to a final one ${\beta }_f$. 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.

16 pages, 3 figures, Submitted to special issue in JSTAT "New Trends in Nonequilibrium Statistical Mechanics: Classical and Quantum Systems (nesmcq18)"