Pressure of a dilute spin-polarized Fermi gas: Lower bound

Abstract

We consider a dilute spin-polarized Fermi gas at positive temperature in dimensions $d\in \{1,2,3\}$. We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order $a^d{\rho }^{2+2/d}$, where $a$ is the $p$-wave scattering length of the repulsive interaction and $\rho$ is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237--260).

34 pages, 1 figure

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• Ground state energy of the dilute spin-polarized Fermi gas: Lower bound

Cited by in corpus (1)

• The Huang-Yang formula for the low-density Fermi gas: upper bound