Abstract
By generalizing our automated algebra approach from homogeneous space to harmonically trapped systems, we have calculated the fourth- and fifth-order virial coefficients of universal spin-1/2 fermions in the unitary limit, confined in an isotropic harmonic potential. We present results for said coefficients as a function of trapping frequency (or, equivalently, temperature), which compare favorably with previous Monte Carlo calculations (available only at fourth order) as well as with our previous estimates in the untrapped limit (high temperature, low frequency). We use our estimates of the virial expansion, together with resummation techniques, to calculate the compressibility and spin susceptibility.
Highlights
At low enough temperatures, or high enough densities, matter invariably displays its quantum mechanical nature, first and foremost by virtue of quantum statistics and due to interaction effects that may alter the nature of the equilibrium state
In this work we investigate the quantum-classical crossover (QCC) of this universal regime using the virial expansion (VE) up to fifth order for a system confined by a harmonic oscillator (HO)
While we restrict ourselves to the unitary limit in those extrapolations, we provide approximate analytic formulas that apply to arbitrary interaction strengths, trap frequency, and spatial dimension
Summary
High enough densities, matter invariably displays its quantum mechanical nature, first and foremost by virtue of quantum statistics (i.e., particles are bosonic or fermionic, at least in three spatial dimensions) and due to interaction effects that may alter the nature of the equilibrium state. There have been attempts to determine b4 at unitarity in the untrapped limit, using measurements of the equation of state [43,44] Those analyses are numerically challenging because one must fit a fourth-order polynomial assuming higher-order contributions are small
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