Density nonlinearities and a field theory for the dynamics of simple fluids

TL;DR

This paper examines the impact of a nonlinear relation constraint in the field theory of simple fluids and finds that it does not alter the dynamics, clarifying the origin of previously observed cutoff mechanisms.

Contribution

The study demonstrates that the nonlinear relation constraint does not change the dynamics, attributing the cutoff mechanism to the $1/\rho$ nonlinearity instead of the constraint itself.

Findings

No change in dynamics due to the constraint

Cutoff mechanism arises from $1/\rho$ nonlinearity

Implications for static properties discussed

Abstract

We study the role of the Jacobian arising from a constraint enforcing the nonlinear relation: ${\bf g}=\rho{\bf V}$, where $\rho,\: {\bf g}$ and ${\bf V}$ are the mass density, the momentum density and the local velocity field, respectively, in the field theoretic formulation of the nonlinear fluctuating hydrodynamics of simple fluids. By investigating the Jacobian directly and by developing a field theoretic formulation without the constraint, we find that no changes in dynamics result as compared to the previous formulation developed by Das and Mazenko (DM). In particular, the cutoff mechanism discovered by DM is shown to be a consequence of the $1/\rho$ nonlinearity in the problem not of the constraint. The consequences of this result for the static properties of the system is also discussed.