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Self-binding of one-dimensional fermionic mixtures with zero-range interspecies attraction
by J. Givois, A. Tononi, and D. S. Petrov
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Submission summary
| Authors (as registered SciPost users): | Jules Givois · Andrea Tononi |
| Submission information | |
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| Preprint Link: | scipost_202211_00027v1 (pdf) |
| Date submitted: | 2022-11-15 17:27 |
| Submitted by: | Givois, Jules |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
For sufficiently large mass ratios the attractive exchange force caused by a single light atom interacting with a few heavy identical fermions can overcome their Fermi degeneracy pressure and bind them into an $N+1$ cluster. Here, by using a mean-field approach valid for large $N$, we find that $N+1$ clusters can attract each other and form a self-bound charge density wave, the properties of which we fully characterize. Our work shows that there are no fundamental obstacles for having self-bound states in fermionic mixtures with zero-range interactions.
Current status:
Reports on this Submission
Report #3 by Anonymous (Referee 3) on 2023-1-6 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202211_00027v1, delivered 2023-01-06, doi: 10.21468/SciPost.Report.6469
Strengths
1. The results are original and timely
2. The work predicts regimes for the existence of self-bound polymers of clusters in an attractive Fermi-Fermi mixture with mass imbalance
3. The theoretical predictions should be testable by available experimental techniques
Weaknesses
1. The validity of mean-field theory is only guaranteed in the large-particle-number regime for the heavy species
2. Results on metastable regimes lack details (see report)
Report
The manuscript investigates the binding of clusters in a Fermi-Fermi mixture with mass imbalance in one spatial dimension by means of mean-field theory. Some of the results for an infinite modulated two-component fluid are obtained by analytical means, while other results for a finite number of light fermions are numerical. The results are interesting and the topic is very timely. The manuscript is well written I have no doubts in the validity of the main results. A limitation of the underlying mean-field theory, as is clearly stated in the manuscript, is that it cannot be expected to provide accurate results for finite particle numbers (of heavy atoms).
The results should definitely be published but I would like the authors to consider the following comments and questions:
Requested changes
1. In section 3 on page 4 a claim is made about the existence of metastable bound states of clusters for finite N_l, e.g. for 1.6 < alpha < 2.3 but it is unclear on which basis this conclusion is drawn as no evidence is presented besides the lines drawn in Fig. 1. Was this conclusion drawn from fully self-consistent numerical calculations, or from the variational analysis? Do we know that these solutions are metastable or might they be (dynamically) unstable solutions of the numerical self-consistent procedure? Why does the corresponding line (e.g. N_l = 2) in Fig. 1 not extend to the full interval of claimed metastability (It looks like the grey dotted line terminates at > 1.8)? Ideally I would like to see a stability analysis of the numerically found non-ground-state solutions, or at least a clarification about what is known about metastability and how the conclusions were reached.
2. The beginning of Sec. 3 on page 3 announces three types of solutions, but the third solution is only mentioned two pages later on page 5. To improve the readability, I would suggest to briefly summarise the character of the three solutions at the beginning of the section before discussing them in detail.
Report #2 by Anonymous (Referee 4) on 2022-12-5 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202211_00027v1, delivered 2022-12-05, doi: 10.21468/SciPost.Report.6257
Strengths
1. The results are original and significant.
2. The theory is detailed, complete and valid.
3. The figures are useful.
Weaknesses
1. The conclusion could be more substantial (see below).
2. There are a number of minor grammatical errors, however these did not impede meaning or alter context.
Report
The study in this paper is based on the phenomenon whereby a single light atom can bind N heavy identical fermions into an N+1 cluster at sufficiently large mass ratios. In isolation, the Pauli exclusion principle (Fermi degeneracy pressure) would prevent the heavier atoms from forming a bound state. However, the lighter particle acts as a mediator that “glues” the (N+1)-body system together by way of an attractive exchange interaction.
Working in one dimension, the authors minimize the density functional to obtain the energy per cluster as a function of a dimensionless parameter “α”, for an increasing number of the light atoms. Here, “α” depends on the ratios of both the numbers and masses of the heavy and light particles. Their main result is that in a special regime of “α”, two such clusters can bind while remaining a finite distance apart — i.e., they maintain a double-peaked density profile. Subsequently, the authors observe this phenomenon of self-binding for higher numbers of clusters, which they show tend to form regular chains or polymers with the number of density peaks equal to the number of light atoms. They analyse the bulk properties of these self-bound chains (or charge density waves) in detail and evoke the Peierls instability to explain the observed density modulation.
The theoretical treatment is very detailed and thorough — there seems to be no missing information — and its testability and relevance to current experiments are also discussed. All aspects and features of the figures are clearly addressed and explained. There are several useful additions appearing in this version of the manuscript compared to the first version that is available on the arXiv. The results on self-binding have important implications for theoretical and experimental studies on mass- and population-imbalanced Fermi-Fermi mixtures, and I would recommend it for publication provided the authors address the following minor remarks.
Requested changes
1. Please add an appropriate reference to the second sentence of the last paragraph of the introduction ([19]?).
2. The conclusion seems a bit brief... I think it would be worth adding a sentence on your findings for only two N+1 clusters (to complement what you say about a polymer of these clusters in the thermodynamic limit). Also, you mention that the small-N problem should be tackled by other methods. Any suggestions of what a useful approach might be in this case?