# A Gaussian theory for fluctuations in simple liquids

## TL;DR

This paper develops a Gaussian-based theoretical framework for modeling density fluctuations in simple liquids, deriving correlation functions that are exact at short times and applicable to confined systems, bridging microscopic details with established theories.

## Contribution

It introduces a Gaussian Hamiltonian approach leading to a linear stochastic equation for density fluctuations, connecting microscopic particle dynamics with macroscopic correlation functions.

## Key findings

- Derived an exact short-time correlation function for density fluctuations.
- Established the relation of the approach to dynamical density functional theory.
- Applicable to confined systems with arbitrary external potentials.

## Abstract

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.