Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas

TL;DR

This paper extends the virial theorem and pressure relations for a strongly correlated two-component Fermi gas to finite scattering lengths and imbalanced populations, broadening the theoretical understanding beyond the unitarity limit.

Contribution

It introduces a generalized virial theorem and pressure relation applicable to finite scattering lengths and population imbalances in Fermi gases.

Findings

Derived a generalized virial theorem for finite scattering lengths.

Extended pressure relations to imbalanced Fermi gases.

Provides theoretical tools for analyzing strongly correlated Fermi systems.

Abstract

For a two-component Fermi gas in the unitarity limit (ie, with infinite scattering length), there is a well-known virial theorem, first shown by J. E. Thomas et al, Phys. Rev. Lett. 95, 120402 (2005). A few people rederived this result, and extended it to few-body systems, but their results are all restricted to the unitarity limit. Here I show that there is a generalized virial theorem for FINITE scattering lengths. I also generalize an exact result concerning the pressure, first shown in cond-mat/0508320, to the case of imbalanced populations.