High-temperature limit of the resonant Fermi gas

Abstract

We use the virial expansion to investigate the behavior of the two-component, attractive Fermi gas in the high-temperature limit, where the system smoothly evolves from weakly attractive fermions to weakly repulsive bosonic dimers as the short-range attraction is increased. We present a new formalism for computing the virial coefficients that employs a diagrammatic approach to the grand potential and allows one to easily include an effective range $R^{\ast }$ in the interaction. In the limit where the thermal wavelength $\lambda \ll R^{\ast }$, the calculation of the virial coefficients is perturbative even at unitarity and the system resembles a weakly interacting Bose-Fermi mixture for all scattering lengths $a$. By interpolating from the perturbative limits $\lambda /|a|\gg 1$ and $R^{\ast }/\lambda \gg 1$, we estimate the value of the fourth virial coefficient at unitarity for $R^{\ast }=0$ and we find that it is close to the value obtained in recent experiments. We also derive the equations of state for the pressure, density and entropy, as well as the spectral function at high temperatures.

18 pages, 12 figures

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Cited by in corpus (5)

• The fourth- and fifth-order virial coefficients from weak-coupling to unitarity
• Spectral density, Levinson's theorem, and the extra term in the second virial coefficient for 1D delta-function potential
• An Effective Series Expansion to the Equation of State of Unitary Fermi Gases
• Normal-state Properties of a Unitary Bose-Fermi Mixture: A Combined Strong-coupling Approach with Universal Thermodynamics
• Virial coefficients expressed by heat kernel coefficients