SciPost Submission Page
Perfect Fluids
by Jan de Boer, Jelle Hartong, Niels A. Obers, Watse Sybesma, Stefan Vandoren
Submission summary
| Authors (as registered SciPost users): | Jelle Hartong · Niels Obers · Stefan Vandoren · Jan de Boer |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1710.04708v3 (pdf) |
| Date accepted: | June 19, 2018 |
| Date submitted: | May 15, 2018, 2 a.m. |
| Submitted by: | Stefan Vandoren |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
List of changes
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.
Published as SciPost Phys. 5, 003 (2018)
Reports on this Submission
Report #3 by Anonymous (Referee 1) on 2018-6-14 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1710.04708v3, delivered 2018-06-14, doi: 10.21468/SciPost.Report.500
Strengths
Weaknesses
Report
Perhaps I can best illustrate the reservation as follows. The authors emphasize that they are treating the velocity as a chemical potential. In fact, I would have said that is the definition of the velocity (as it appears in e.g. their 2.1), and it's certainly not new. Given this fact, it is obvious that in the absence of boost symmetries the pressure will depend on the velocity. Relatedly, while it's conceivable that 2.10 has never been written down in this form (as the authors claim somewhat boldly in footnote 3 -- have they checked every paper in existence?), in any case it's a trivial consequence of the above fact. On this point, and this just happens to be one paper that I know off the top of my head, the authors may find equation 9 of https://arxiv.org/abs/0809.4870 instructive. Chi in that equation is the superfluid velocity squared, which is indeed not associated to a boost symmetry, and so this equation has a rather strong analogy to 2.9 in the paper under review. Obviously the equations are not the same equation, one has to do with superfluids and the other doesn't, but the point is that once thermodynamics can depend on a velocity this kind of relation is a rather immediate thing that drops out.
Perhaps I would mind less if the authors were able to present these points without claiming novelty at every turn. The word "new" appears 16 times in the paper. Some journals have a policy of not allowing explicit use of "new" and "novel" etc., and perhaps that would help here.
Report #2 by Anonymous (Referee 3) on 2018-6-5 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1710.04708v3, delivered 2018-06-05, doi: 10.21468/SciPost.Report.491
Strengths
Weaknesses
Report
Regarding the newness of (2.10), I would point out that a similar quantity shows up in the hydrodynamics of superfluids, where v is replaced by the gradient of the phase of the order parameter. I wonder if (2.10) may show up more generally in the hydrodynamics of two-component fluids.
Requested changes
1) On page 3, mention is made of ``various places in the literature''. It would be nice to know what these places are.
2) On page 21, there is a similar issue with the statement ``We give references below''. There are a handful of references to older papers in what follows, but too much work is left to the reader. It would be nice to have a couple of specific sentences outlining what is new here and what is drawn from the literature, with equation numbers.
3) I noticed a handful of typos, indepenent'' on p 11,one can be build'' on p 17.
Report #1 by Anonymous (Referee 2) on 2018-6-3 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1710.04708v3, delivered 2018-06-03, doi: 10.21468/SciPost.Report.485
Strengths
Weaknesses
Report
(I did not say that there was absolutely nothing new in Section 4. In fact the authors ended up doing mostly what I wanted, which was to focus on the z\ne 1,2 limits in a more streamlined section.)
I had a typo in my earlier review which was that I wrote to talk about "large z" limit but that should have been "large v" limit, although I suppose both are worthwhile -- since this is clearly my "fault" I would not bother the authors to add this to the paper unless they felt compelled to.
I think the paper can be published as is.
Thank you for the positive recommendation.
Anonymous on 2018-06-06 [id 267]
(in reply to Report 2 on 2018-06-05)We find the comments of this referee difficult to place in context. Firstly, whether this manuscript reminds the referee of some other journal style, we do not find a very useful comment that we can do something with. Secondly, the referee has a suspicion that most part is not new, but we do not know how to respond to 'suspicion'. The comment about the "newness" of equation (2.10) is a mystery to us, as the velocity is not the gradient of the phase of an order parameter. We do agree though that is interesting to apply our framework to superfluids, as we mention in the discussion and outlook.
As for the requested changes, we believe we have stressed very clearly and explicitly in section 4 what are for sure the new equations, namely the velocity dependent terms in the partition function and thermodynamic quantities, and the speed of sound. We have given the relevant references [32,33] and connected them to e.g. the relevant equations. Some results where known for z=2, but the other referee asked us to take out this special case. Still reference [33] is mentioned connected to eqn (4.45). Whether e.g. the formula for the heat capacity in eqn (4.12) is new, we don't know and we make no strong claims there. We have not found it anywhere in the literature, but agree it is a straightforward generalisation, as we write in the beginning of section 4.
We would be happy to correct the typos the referee mentions in a later stage.