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Perfect Fluids

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

Submission summary

As Contributors: Jan de Boer · Stefan Vandoren · Niels Obers
Arxiv Link: https://arxiv.org/abs/1710.04708v3
Date submitted: 2018-05-15
Submitted by: Vandoren, Stefan
Submitted to: SciPost Physics
Domain(s): Theoretical
Subject area: Fluid Dynamics

Abstract

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 energy-momentum 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 (non-relativistic) 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.

Current status:
Editor-in-charge assigned


List of changes

Changes/Modifications in the Draft:

1) Abstract/Intro: changed the phrasing “develop a new theory” into “present a systematic or unified analysis/treatment/framework”.
2) Added in intro and in section 2 a few sentences mentioning that the notion of kinetic mass density was already discussed in the literature (e.g. review 1612.07324), but at the same time stress that this was at zero velocity (lab frame), whereas we want to know it in all frames. Moreover, we stressed in the intro that this kinetic mass density follows from the pressure at finite velocity. Therefore, it is important to determine velocity dependent terms.
3) Streamlined in the intro better the three main new results obtained in this paper, stressing also the unified picture we give that can be applied to all perfect fluids with and without boost symmetry.
4) Restructured Section 3, and moved previous section 3.2 (boosted fluids) to an appendix.
5) Major editing in Section 4: deleted all the discussion of the special values of z=1 and z=2, such that the exposition is shorter and flows more smoothly. Furthermore, we added some more text about the velocity dependent terms, for instance in the pressure.
6) Added a discussion about the large z-limit, and the velocity dependent terms in that limit, also in Section 4.

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