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Virial expansion coefficients in the unitary Fermi gas

by Shimpei Endo

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Submission summary

As Contributors: Shimpei Endo
Preprint link: scipost_201910_00037v1
Date submitted: 2019-10-24 02:00
Submitted by: Endo, Shimpei
Submitted to: SciPost Physics Proceedings
Proceedings issue: 24th European Few Body Conference (University of Surrey, U.K.)
Academic field: Physics
  • Atomic, Molecular and Optical Physics - Theory
  • Condensed Matter Physics - Theory
Approach: Theoretical


Virial expansion is widely used in cold atoms to analyze high temperature strongly correlated many-body systems. As the n-th order virial expansion coefficient can be accurately obtained by exactly solving up to n-body problems, the virial expansion offers a few-body approach to study strongly correlated many-body problems. In particular, the virial expansion has successfully been applied to unitary Fermi gas. We review recent progress of the virial expansion studies in the unitary Fermi gas, in particular the fourth order virial coefficient.

Current status:
Has been resubmitted

Submission & Refereeing History

Resubmission scipost_201910_00037v2 on 18 December 2019

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Submission scipost_201910_00037v1 on 24 October 2019

Reports on this Submission

Anonymous Report 1 on 2019-12-12 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_201910_00037v1, delivered 2019-12-12, doi: 10.21468/SciPost.Report.1389


The author reviews the study of virial expansion in a unitary Fermi gas.
The general background of the virial expansion is clearly explained in the connection with few-body and many-body physics.

I recommend the publication of this article after addressing following issues.

1) In the introduction, the author mentions that a unitary Fermi gas is relevant for understanding neutron stars.
I think that more detailed explanation with some references is required because the system scales are quite different between these two systems.
While the scattering length in cold atoms is generally the order of nano(or micro)-meters, the neutron-neutron scattering length is -18.5 femto-meters.

2) Since the virial expansion itself cannot directly be applied to neutron star physics where the temperature is quite low, I suggest the author additionally refer to the supernova matter at finite temperature.
In Phys. Rev. C 96, 055804 (2017), a neutrino-nucleon scattering properties have been derived from the 4th virial expansion of a unitary Fermi gas.

3) I think that Eqs. (2)-(4) for the virial equation of state should explicitly involve the 4-th order coefficient b_4 since in the latter part the author reviews b_4.

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