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 * in the interaction. In the limit where the thermal wavelength λ R * , 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 λ/|a| 1 and R * /λ 1, we estimate the value of the fourth virial coefficient at unitarity for R * = 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.

The interaction-sensitive states of a trapped two-component ideal Fermi gas and application to the virial expansion of the unitary Fermi gas

“…This leaves the possibility that the conjecture is correct for ∆B 3,1 . Incidentally, itsω → 0 + limit ∆B old conj 3,1 (0 + ) = 0.02297(4) [20] is close to the prediction 0.025 of the approximate diagrammatic method of reference [38] (this value was communicated to us privately by Jesper Levinsen). For 2 + 2 fermions, the conjectured values (94) clearly disagree with the blue dashed-dotted lines even in the cut-off unaffected regionω ≥ 1 and with the approximate value ∆B 2,2 (0 + ) = −0.036 of reference [38], by a factor close to 2.…”

“…In the equation (108) (0 + ) = −0.0305(2) is of the same order as the approximate value ∆B 2,2 (0 + ) = −0.036 of reference [38]. There is therefore a good possibility that the new conjecture for ∆B 2,2 is exact.…”

Spectral density, Levinson's theorem, and the extra term in the second virial coefficient for the one-dimensional δ -function potential

“…Various techniques have been developed for perturbatively calculating virial coefficients from field theory [16,[28][29][30]. In particular, we will employ the technique developed in [16], which expands the many-body propagator in powers of fugacity and works directly in imaginary time instead of frequency.…”

Normal-State Properties of a Unitary Bose–Fermi Mixture: A Combined Strong-Coupling Approach with Universal Thermodynamics

“…is the lowest-order hetero-pair correlation function, where f s (x) is the Bose (s=B) and Fermi virial expansion, [49][50][51][52][53][54][55][56] when T/T F > ∼ 3 (where T F is the Fermi temperature of N Fermi atoms). In this high-temperature expansion, the number equations are given by,…”