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Pressure of a dilute spin-polarized Fermi gas: Upper bound
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abstract
We prove an upper bound on the pressure of a dilute fully spin-polarized Fermi gas capturing the leading correction to the pressure of a free gas resulting from repulsive interactions. This correction is of order $a^3\rho^{8/3}$, with $a$ the $p$-wave scattering length of the interaction and $\rho$ the particle density, depends on the temperature and matches the corresponding lower bound of [arXiv:2307.01113].
Forward citations
Cited by 3 Pith papers
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The second order Huang-Yang approximation to the Fermi thermodynamic pressure
The pressure of a dilute Fermi gas is shown to match the Huang-Yang second-order formula up to a temperature that is optimal by scaling, with an explicit positive-temperature correction.
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The Huang-Yang conjecture for the low-density Fermi gas
For dilute spin-1/2 Fermi gases with repulsive short-range interactions, the ground state energy density equals the free Fermi term plus 8πa ρ↑ρ↓ plus the Huang-Yang a²ρ^{7/3} correction, with error o(ρ^{7/3}).
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Momentum Distribution of a Fermi Gas with Coulomb Interaction in the Random Phase Approximation
A rigorous proof shows the momentum distribution of a Fermi-gas trial state is the Fermi step plus the RPA correction, with k_F^{-2+ε} errors for summable interactions.
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