Energetics of a strongly correlated Fermi gas

Annals of Physics

Volumn 323, Issue 12, 2008, Pages 2952-2970

  Tan, Shina ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

BEC BCS crossover; Energy; Momentum distribution; s Wave contact interaction

Indexed keywords

EID: 54849428140     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2008.03.004     Document Type: Article

References (29)

1. ↑) exceeds 13.6, the three-body Efimov effect appears [18], the two-body pseudopotential is no longer sufficient, and the formalism in this paper can no longer be applied without qualitative modifications and/or extensions.
2. We let ℏ = 1 for conciseness, and the term "wave vector" is used interchangeably with "momentum". ℏ is restored when contact with experiments is made.
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4. Leggett A.J. Modern Trends in the Theory of Condensed Matter (1980), Springer Verlag, Berlin pp. 13-27
5. The BEC-BCS crossover is not restricted to a Fermi gas with resonant contact interaction characterized by the s-wave scattering length, although the latter system is the most popular, and this paper is restricted to this minimal model.
6. See, e.g., L. Viverit et al., Phys. Rev. A 69, 013607 (2004), in particular its footnote 31.
7. l (k) (l ≥ 1) is no longer negligible.
8. * is small, our calculations are directly applicable.
9. Periodic boundary condition is used. In the case of a uniform gas, Ω is the volume of the uniform system; in the case of a confined gas, Ω is any volume which greatly exceeds the actual spatial extension of the gas.
10. k σ is solely caused by interparticle interactions.
11. To appreciate this general feature, it is instructive to consider two interacting fermions confined in a box.
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13. 1 is the total internal energy (kinetic energy plus interfermionic interaction energy) divided by the number of fermions, in the center-of-mass frame of the Fermi gas.
14. internal, discussed in this paper includes the bulk kinetic energy, if the whole system is in a motion.
15. There are other attempts to formulate the same problem. Most of them are aimed at a mean-field approximation, in contrast with this paper. An alternative approach that is of the same simplicity has yet been seen.
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24. The vacuum state and the single-fermion states also belong to the physical subspace. Any linear combination of any two states which belong to P also belongs to P and is physically allowed.
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