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The European Physical Journal B

Particle densities for dilute hard-sphere Bose or Fermi gases in an external potential

X.-Z. Wang

Published Dec 1, 2005• 4 citations
Publisher
DOI
10.1140/epjb/e2005-00414-x

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The Ühling-Uhlenbeck equations and the discrete velocity model are used to study the propagation of plane waves in a dilute system of Bose particles with hard-sphere interactions. The Ühling-Uhlenbeck collision sum, as it is highly nonlinear, is first linearized and then decomposed by using the plane wave assumption. We address the dispersion relations thus obtained by the relevant parameter θ or B which describes the Bose particles for the quantum analogue of the discrete Boltzmann system when B is positive (and θ = 1). The attenuation of plane waves propagating in dilute Bose gases in the low density or temperature regime shows a rather sharp change which is completely different from that in dilute Boltzmann gases.
Itinerant ferromagnetism in dilute Fermi gases is predicted to emerge at values of the gas parameter where second-order perturbation theory is not accurate enough to properly describe the system. We have revisited perturbation theory for SU(N) fermions and derived its generalization up to third order both in terms of the gas parameter and the polarization. Our results agree satisfactorily with quantum Monte Carlo results for hard-sphere and soft-sphere potentials for S = 1/2 S = 1 / 2 . Although the nature of the phase transition depends on the interaction potential, we find that for a hard-sphere potential a phase transition is guaranteed to occur. While for S= 1/2 S = 1 / 2 we observe a quasi-continuous transition, for spins 3/2 3 / 2 and 5/2 5 / 2 , a first-order phase transition is found. For larger spins, a double transition (combination of continuous and discontinuous) occurs. The critical density reduces drastically when the spin increases, making the phase transition more accessible to experiments with ultracold dilute Fermi gases. Estimations for Fermi gases of Yb and Sr with spin 5/2 5 / 2 and 9/2 9 / 2 , respectively, are reported.