Dynamics of uctuations in the Gaussian model with dissipative Langevin Dynamics

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 > sc (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 condensation of fluctuations. We show that the probability of fluctuations with s < inft[sc (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 > inft[sc (t)], instead, displays a slow and more complex behavior, because the macroscopic population of the condensing degree of freedom is involved.