## SciPost Submission Page

# Hydrodynamic Modes of Homogeneous and Isotropic Fluids

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

#### - Published as SciPost Phys. 5, 014 (2018)

### 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 |

Discipline: | Physics |

Subject area: | Fluid Dynamics |

Approach: | Theoretical |

### 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.

### Ontology / Topics

See full Ontology or Topics database.Published as SciPost Phys. 5, 014 (2018)

### 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.

### Submission & Refereeing History

- Report 2 submitted on 2018-06-22 18:40 by
*Anonymous* - Report 1 submitted on 2018-05-30 16:24 by
*Anonymous*

## Reports on this Submission

### Anonymous Report 2 on 2018-6-22 Invited Report

### Report

I am satisfied with the changes, and approve the resubmitted version.

### Anonymous Report 1 on 2018-5-30 Invited Report

### Report

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