An Effective Series Expansion to the Equation of State of Unitary Fermi Gases
arXiv:1607.04273 · doi:10.1088/0953-4075/49/22/225301
Abstract
Using universal properties and a basic statistical mechanical approach, we propose a general equation of state for unitary Fermi gases. The universal equation of state is written as a series solution to a self consistent integral equation where the general solution is a linear combination of Fermi functions. First, by truncating our series solution to four terms with already known exact theoretical inputs at limiting cases, namely the first \emph{three} virial coefficients and using the Bertsch parameter as a free parameter, we find a good agreement with experimental measurements in the entire temperature region in the normal state. This analytical equation of state agrees with experimental data up to the fugacity , which is a vast improvement over the other analytical equations of state available where the agreements is \emph{only} up to . Second, by truncating our series solution to four terms again using first \emph{four} virial coefficients, we find the Bertsch parameter , which is in good agreement with the direct experimental measurement of . This second form of equation of state shows a good agreement with self-consistent T-matrix calculations in the normal phase.
arXiv commentSeven pages with two figure. Published version
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