Abstract
Virial expansion is widely used in cold atoms to analyze high temperature strongly correlated many-body systems. As the n-th order virial expansion coefficient can be accurately obtained by exactly solving up to n-body problems, the virial expansion offers a few-body approach to study strongly correlated many-body problems. In particular, the virial expansion has successfully been applied to unitary Fermi gas. We review recent progress of the virial expansion studies in the unitary Fermi gas, in particular the fourth order virial coefficient.
Highlights
As the s-wave scattering length between the neutrons ann ≈ −23 fm [8,9] is so large that they can be approximately regarded as the unitary Fermi system, the knowledge of the equation of state of the unitary Fermi gas is relevant for understanding neutron stars [2, 3, 48,49,50,51]
We review the virial expansion of the equation of state of the unitary Fermi
The unitary Fermi gas has been realized in cold atom experiments, and its universal equation of state has been observed
Summary
The thermodynamic potential Ω of the many-body system is expanded as [41, 85]. Even after accurately solving few-body problems and obtaining all the energy eigenvalues, we still need to take the canonical partition sum of them. They include the bound states, and highly degenerate continuum states. Hyper-radial and hyper-angular equations become separable for a unitary Fermi gas since the system is scale invariant [7] This facilitates solving few-body problem in this system both numerically and analytically. Using analytical solutions of the unitary three-body system in the harmonic trap [78], Liu, Hu, and Drummond have accurately obtained b3 of the unitary Fermi gas to be b3 = −0.29095295 [79] after extrapolating it to a homogeneous system.
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