Concavity of the collective excitation branch of a Fermi gas in the BEC-BCS crossover

Abstract : We study the concavity of the dispersion relation $q\mapsto \omega_{\mathbf{q}}$ of the bosonic excitations of a three-dimensional spin-$1/2$ Fermi gas in the Random Phase Approximation (RPA). In the limit of small wave numbers $q$ we obtain analytically the spectrum up to order $5$ in $q$. In the neighborhood of $q=0$, a change in concavity between the convex BEC limit and the concave BCS limit takes place at $\Delta/\mu\simeq0.869$ [$1/(k_F a)\simeq-0.144$], where $a$ is the scattering length between opposite spin fermions, $k_F$ is the Fermi wave number and $\Delta$ the gap according to BCS theory, and $\mu$ is the chemical potential. At that point the branch is concave due to a negative fifth-order term. Our results are supplemented by a numerical study which shows the evolution of the border between the zone of the $(q,\Delta)$ plane where $q\mapsto \omega_{\mathbf{q}}$ is concave and the zone where it is convex.
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Contributor : Yvan Castin <>
Submitted on : Tuesday, January 26, 2016 - 10:47:19 AM
Last modification on : Thursday, February 20, 2020 - 12:34:30 PM
Long-term archiving on: Wednesday, April 27, 2016 - 1:21:11 PM

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H Kurkjian, Yvan Castin, A Sinatra. Concavity of the collective excitation branch of a Fermi gas in the BEC-BCS crossover. Physical Review A, American Physical Society, 2016, 93, pp.013623. ⟨10.1103/PhysRevA.93.013623⟩. ⟨hal-01228798v2⟩

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