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Collective oscillations of a twocomponent Fermi gas on the repulsive branch
by Tomasz Karpiuk, Piotr T. Grochowski, Mirosław Brewczyk, Kazimierz Rzążewski
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Submission summary
Authors (as registered SciPost users):  Piotr T. Grochowski · Kazimierz Rzążewski 
Submission information  

Preprint Link:  https://arxiv.org/abs/1908.07771v2 (pdf) 
Date submitted:  20191121 01:00 
Submitted by:  Grochowski, Piotr T. 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We calculate frequencies of collective oscillations of twocomponent Fermi gas that is kept on the repulsive branch of its energy spectrum. Not only is a paramagnetic phase explored, but also a ferromagnetically separated one. Both in, and outofphase perturbations are investigated, showing contributions from various gas excitations. Additionally, we compare results coming from both timedependent HartreeFock and densityfunctional approaches.
Current status:
Reports on this Submission
Anonymous Report 2 on 2020224 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1908.07771v2, delivered 20200224, doi: 10.21468/SciPost.Report.1527
Strengths
1clear and well written article
2 TImely work
3 comparison with hydrodynamics and sum rule approaches
Weaknesses
1 choice of the trap geometry leading to misleading conclusion about comparison between hydrodynamics and TDHF
Report
In this article, the authors study the dynamics of a repulsive mixtures of fermionic gases confined in an isotropic trap within HartreeFock’s approximation. They focus on the lowest quadrupolar modes and consider identical and opposite excitations on the two species. The results are then compared to hydrodynamic approaches.
This article is interesting, clear and well written and the reported results are timely since the experimental study of repulsive Fermi gases is currently under way and is still largely open.
One shortcoming of the work though is the choice of a highly degenerate trap geometry that may lead to misleading conclusions if one wants to transpose the results of this work to more relevant trapping geometries (usually traps are anisotropic and more often than not strongly elongated). Indeed, one of the conclusions of the authors is that TDHF agrees with hydrodynamics (except for the quadrupole). This agreement is in my opinion coincidental and purely a consequence of the choice of trap. Indeed, if one considers an elongated trap, the prediction for the quadrupole modes of a weakly interacting gas is essentially twice the trapping frequencies. By contrast, hydrodynamics for instance predicts for the axial breathing mode a frequency equal to (12/5)^(1/2) times the axial trapping frequency. Conversely, is there a deep reason why hydrodynamics should be applicable to a weakly interacting gas in an isotropic trap?
Moreover, it would be interesting to compare the oscillation frequencies of the different modes, since it seems to me that the upper branches of all graphs are essentially all the same (this is pointed out when discussing symmetric vs antisymmetric excitation of the monopole compression mode, but I didn’t see it stated for the other modes). I have the impression that there are only three independent frequencies. Can the authors confirm? And if so, is there a simple explanation?
Finally, the numerical resolution of 3D nonlinear PDE being notoriously challenging, can the authors provide more details about the implementation of their numerical scheme (grid size, solver…)?
Requested changes
1clarify the role of the trap geometry
2 Explicitely compare the oscillation frequencies
3 Provide more details on numerical implementation.
Anonymous Report 1 on 20191211 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1908.07771v2, delivered 20191211, doi: 10.21468/SciPost.Report.1388
Strengths
1) The manuscript contains new physics: the authors investigate the frequencies of collective oscillations of twocomponent Fermi gas, for repulsive interactions.
Weaknesses
1) Some points are unclear.
2) The quality of Figs. 38 is poor.
Report
In this paper the authors presents a theoretical study of the frequencies of collective oscillations of twocomponent Fermi gas, on the repulsive branch of its energy spectrum. The analysis is carried out by means of some approximation, and for a limited number of particles (2 x 56), well below the typical numbers available in the experiments. Notwithstanding, the results may be interesting for the community working on this subject.
Before I can make a final recommendation, the author should consider the following points.
1) In equation (1) the authors employ a notation where the coordinates x_i refer to "both spatial and spin variables", but soon after they change to a different notation, with explicit indices for spin variables, and with an explicit dependence on time. I would suggest to unify the notation, for the sake of clarity.
2) The Fourier transform, which enters the discussion from pag. 7 on, it is never defined. Please include an explicit definition (in terms of formulas, I mean).
3) Figs. 38 have two problems, at least. They use much space, and this result in a dispersion of information. I would suggest to collect them in a _single_ figure, with different panels, restricting the horizontal axis up to k_F*a=1 (nothing is plotted beyond that limit). Then, what are those blueish in Figs. 3,6,8? maybe the FT? It is totally unclear and aesthetically poorly plotted. Please revise the figure carefully.
4) The sentence "Recapitulating, we have filled the gap in the literature" (in the conclusions) is excessively presumptuous, I would suggest to remove it.
5) The English needs some revision. In particular, please check carefully the use of articles.
Requested changes
1) Unify the notation of equations (1)(3).
2) Define qualitatively the Fourier transform.
3) Revise Figs. 38 (see report).
4) Avoid presumptuous claims.
5) Revise the English.
Author: Piotr T. Grochowski on 20200331 [id 783]
(in reply to Report 1 on 20191211)
We thank the Referee for the favourable report and insightful remarks. We believe that with a revised manuscript we satisfactorily answer the issues raised in the report.

We unified the notation, changing the manybody wave function to express the spatial orbitals explicitly.

We included explicit definitions of quantities we plot in the backgrounds of different panels in Fig. 3.

We revised Figs. 38: We compiled them into one figure, added full legends and interpolated the Fourier transforms data to have a smooth background. However, we did not decide to remove data from the phaseseparated regime as we believe it presents physically valuable results.

We removed said sentence and checked for additional presumptuous statements in the text.

We improved the language throughout the text.
Author: Piotr T. Grochowski on 20200331 [id 784]
(in reply to Report 2 on 20200224)We thank the Referee for the positive report and valuable comments. We incorporated requested changes into the manuscript.
We believe that with introductory paragraph in that section, describing the usual applicability of hydrodynamics and its problems with noninteracting gas and with the last paragraph that explicitly comments on regimes in which we can use the framework:
we state the regime of applicability of the method clearly enough.
We added a plot in which we directly compare frequency branches in different cases, showing that there are only three prototypical collective excitations under the perturbation schemes we checked.
At the end of the introductory paragraph of Section 2, we added a paragraph with details of numerics.