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.

Correlations and forces in sheared fluids with or without quenching

“…. This is a remnant of equation (33), which shows that higher orders in shear are important at late times. Shear thus appears to dominate forces at late times.…”

“…The core results of this section are equations (33) and (35), which provide the time dependent post-quench correlation functions in the presence of (weak) shear to zeroth and quadratic order in x x | |, respectively. In particular, equation (33) will be used to compute forces (see section 6).…”

“…(Here we do not consider the presence of long-ranged forces such as van der Waals forces, which asymptotically give rise to an algebraic decay of correlation functions). Within the Gaussian approximation, m in equation (1) can be expressed in terms of the isothermal compressibility V P V T T c = - ¶ ¶ ( ) [33,58,59] (V is the system volume):…”

“…In general, they do not point along the axis connecting the centers of the small inclusions considered to be embedded in the fluctuating medium. Since quenches or shearing appear to be realizable in a variety of systems with conserved particle number, including active matter, we expect these findings to be relevant for experimental investigations.instance, to uniaxial magnetic systems, model B describes binary alloys, spinodal dynamics of binary liquid mixtures, as well as single-component fluids [32,33]. These models have been applied extensively in describing various dynamical situations, e.g.…”

“…instance, to uniaxial magnetic systems, model B describes binary alloys, spinodal dynamics of binary liquid mixtures, as well as single-component fluids [32,33]. These models have been applied extensively in describing various dynamical situations, e.g.…”