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Hydrodynamic Modes of Homogeneous and Isotropic Fluids

by Jan de Boer, Jelle Hartong, Niels A. Obers, Watse Sybesma, Stefan Vandoren

Submission summary

As Contributors: Jelle Hartong · Niels Obers · Jan de Boer
Arxiv Link: https://arxiv.org/abs/1710.06885v2
Date accepted: 2018-07-16
Date submitted: 2018-05-15
Submitted by: Obers, Niels
Submitted to: SciPost Physics
Domain(s): Theoretical
Subject area: Fluid Dynamics

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.

Current status:

Ontology / Topics

See full Ontology or Topics database.

Dissipative transport Dynamical exponents Hydrodynamics Lorentz invariance Navier-Stokes equation Relativistic fluids Shear viscosity Thermal conductivity Transport

List of changes

1) In the 4th paragraph of the introduction we have added some sentences stressing that already
at the perfect fluid level (as shown in Ref.[1]) there are now results (such as novel expressions for the speed of sound), which
may be observable.

2) In regard concrete applications we have added the very recent Ref. [21] (on viscous electron fluid) which in fact is a concrete
example of non-boost invariant system to which our framework applies. (This is mentioned at the very end of the Introduction, section 1)

3) We have added in the 2nd paragraph of Section 2 more details on the form of the perfect fluid energy momentum tensor.

4) We have also updated the citation Ref.[9] with publication data.


Reports on this Submission

Anonymous Report 2 on 2018-6-22 Invited Report

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Anonymous Report 1 on 2018-5-30 Invited Report

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The authors have addressed my concerns. I approve of publication in this journal.

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