# Dynamics of fluctuations in the Gaussian model with conserved dynamics

## TL;DR

This paper investigates the fluctuation dynamics of a conserved Gaussian model after a temperature quench, revealing a critical variance threshold that determines condensation-like behavior and non-equilibrium relaxation patterns.

## Contribution

It introduces a detailed analysis of fluctuation-induced condensation and slow dynamics in a conserved Gaussian model following a thermal quench.

## Key findings

- Existence of a critical variance $s_c(t)$ separating different fluctuation regimes.
- Rapid convergence of fluctuations below the critical threshold to a stationary state.
- Slow non-equilibrium dynamics associated with zero wavevector mode population above the threshold.

## 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.