Dynamics of fluctuations in the Gaussian model with dissipative Langevin Dynamics

Abstract

We study the dynamics of the fluctuations of the variance $s$ of the order parameter of the Gaussian model, following a temperature quench of the thermal bath. At each time $t$, there is a critical value $s_c(t)$ of $s$ such that fluctuations with $s>s_c(t)$ are realized by condensed configurations of the systems, i.e., a single degree of freedom contributes macroscopically to $s$. This phenomenon, which is closely related to the usual condensation occurring on average quantities, is usually referred to as {\it condensation of fluctuations}. We show that the probability of fluctuations with $s<\inf_t [s_c(t)]$, associated to configurations that never condense, after the quench converges rapidly and in an adiabatic way towards the new equilibrium value. The probability of fluctuations with $s>\inf_t [s_c(t)]$, instead, displays a slow and more complex behavior, because the macroscopic population of the condensing degree of freedom is involved.