Jan de Boer, Jelle Hartong, Niels A. Obers, Watse Sybesma, Stefan Vandoren
SciPost Phys. 5, 014 (2018) ·
published 13 August 2018

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Relativistic fluids are Lorentz invariant, and a nonrelativistic limit of
such fluids leads to the wellknown NavierStokes 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
nonrelativistic 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 NavierStokes equation and determine all dissipative
and nondissipative 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.
Jan de Boer, Jelle Hartong, Niels A. Obers, Watse Sybesma, Stefan Vandoren
SciPost Phys. 5, 003 (2018) ·
published 17 July 2018

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We present a systematic treatment of perfect fluids with translation and rotation symmetry, which is also applicable in the absence of any type of boost symmetry. It involves introducing a fluid variable, the {\em kinetic mass density}, which is needed to define the most general energymomentum tensor for perfect fluids. Our analysis leads to corrections to the Euler equations for perfect fluids that might be observable in hydrodynamic fluid experiments. We also derive new expressions for the speed of sound in perfect fluids that reduce to the known perfect fluid models when boost symmetry is present.
Our framework can also be adapted to (nonrelativistic) scale invariant fluids with critical exponent $z$. We show that perfect fluids cannot have
Schr\"odinger symmetry unless $z=2$. For generic values of $z$ there can be fluids with Lifshitz symmetry, and as a concrete example, we work out in detail the thermodynamics and fluid description of an ideal gas of Lifshitz particles and compute the speed of sound for the classical and quantum Lifshitz gases.
Prof. Obers: "We thank the referees for thei..."
in Report on Hydrodynamic Modes of Homogeneous and Isotropic Fluids