## SciPost Submission Page

# Collective oscillations of a two-component Fermi gas on the repulsive branch

### by Tomasz Karpiuk, Piotr T. Grochowski, Mirosław Brewczyk, Kazimierz Rzążewski

### Submission summary

As Contributors: | Piotr Grochowski |

Arxiv Link: | https://arxiv.org/abs/1908.07771v2 |

Date submitted: | 2019-11-21 |

Submitted by: | Grochowski, Piotr |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Atomic, Molecular and Optical Physics - Theory |

Approach: | Theoretical |

### Abstract

We calculate frequencies of collective oscillations of two-component 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 out-of-phase perturbations are investigated, showing contributions from various gas excitations. Additionally, we compare results coming from both time-dependent Hartree-Fock and density-functional approaches.

###### Current status:

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 1 on 2019-12-11 Invited Report

### Strengths

1) The manuscript contains new physics: the authors investigate the frequencies of collective oscillations of two-component Fermi gas, for repulsive interactions.

### Weaknesses

1) Some points are unclear.

2) The quality of Figs. 3-8 is poor.

### Report

In this paper the authors presents a theoretical study of the frequencies of collective oscillations of two-component 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. 3-8 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. 3-8 (see report).

4) Avoid presumptuous claims.

5) Revise the English.