Hydrodynamic Modes of Homogeneous and Isotropic Fluids

TL;DR

This paper develops a comprehensive hydrodynamic framework for homogeneous, isotropic fluids lacking Lorentz invariance, deriving new transport coefficients and dispersion relations applicable to a broad class of non-relativistic and critical systems.

Contribution

It provides the first full treatment of hydrodynamics for such fluids, including new expressions for sound speed, transport coefficients, and mode dispersion relations.

Findings

Derived new expressions for the speed of sound.

Calculated corrections to Navier-Stokes equations.

Determined dispersion relations for hydrodynamic modes.

Abstract

Relativistic fluids are Lorentz invariant, and a non-relativistic limit of such fluids leads to the well-known Navier-Stokes equation. However, for fluids moving with respect to a reference system, or in critical systems with generic dynamical exponent z, the assumption of Lorentz invariance (or its non-relativistic version) does not hold. We are thus led to consider the most general fluid assuming only homogeneity and isotropy and study its hydrodynamics and transport behaviour. Remarkably, such systems have not been treated in full generality in the literature so far. Here we study these equations at the linearized level. We find new expressions for the speed of sound, corrections to the Navier-Stokes equation and determine all dissipative and non-dissipative first order transport coefficients. Dispersion relations for the sound, shear and diffusion modes are determined to second order in momenta. In the presence of a scaling symmetry with dynamical exponent z, we show that the sound attenuation constant depends on both shear viscosity and thermal conductivity.