A Gaussian theory for fluctuations in simple liquids

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.

8 pages

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• Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson-Nernst-Planck models and its relevance to correlation function analysis
• Transverse density fluctuations around the ground state distribution of counterions near one charged plate: stochastic density functional view
• Stochastic dynamics and thermodynamics around a metastable state based on the linear Dean-Kawasaki equation
• Non-hyperuniform metastable states around a disordered hyperuniform state of densely packed spheres: stochastic density functional theory at strong coupling
• Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation
• Correlations and forces in sheared fluids with or without quenching
• Viscosity of a sheared correlated (near-critical) model fluid in confinement
• Nonequilibrium mixture dynamics: A model for mobilities and its consequences
• Mobility-induced kinetic effects in multicomponent mixtures
• Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation
• Dynamics of soft interacting particles on a comb
• Solving Lyapunov equations for electrically driven ternary electrolytes -- application to long-range van der Waals interactions
• Macroscopic fluctuation theory of interacting Brownian particles