Quasiclassical molecular dynamics for the dilute Fermi gas at unitarity

TL;DR

This paper employs molecular dynamics with an effective quantum potential to study the dilute Fermi gas at unitarity, providing insights into its equation of state, pair correlations, and shear viscosity, including higher order corrections.

Contribution

It introduces a quasiclassical molecular dynamics approach with an effective quantum potential to analyze the dilute Fermi gas at unitarity, extending understanding beyond the dilute, high-temperature limit.

Findings

Results interpolate between second and third order virial expansions.

Excellent agreement with T-matrix calculations for contact density.

Reproduces expected shear viscosity scaling at high temperature.

Abstract

We study the dilute Fermi gas at unitarity using molecular dynamics with an effective quantum potential constructed to reproduce the quantum two-body density matrix at unitarity. Results for the equation of state, the pair correlation function and the shear viscosity are presented. These quantities are well understood in the dilute, high temperature, limit. Using molecular dynamics we determine higher order corrections in the diluteness parameter $n\lambda^3$, where $n$ is the density and $\lambda$ is the thermal de Broglie wave length. In the case of the contact density, which parameterizes the short distance behavior of the correlation function, we find that the results of molecular dynamics interpolates between the truncated second and third order virial expansion, and are in excellent agreement with existing T-matrix calculations. For the shear viscosity we reproduce the expected scaling behavior at high temperature, $\eta\sim 1/\lambda^3$, and we determine the leading density dependent correction to this result.