Universal high-momentum asymptote and thermodynamic relations in a spinless Fermi gas with a resonant $p$-wave interaction

TL;DR

This paper explores universal relations in a spinless Fermi gas near a $p$-wave resonance, revealing a $k^{-2}$ momentum asymptote, the physical significance of the $p$-wave contact, and its dependence on interaction details.

Contribution

It establishes the asymptotic behavior of the momentum distribution and proves the adiabatic sweep theorem for $p$-wave resonances, clarifying the physical meaning of the $p$-wave contact.

Findings

Momentum distribution asymptote proportional to $k^{-2}$.

$p$-wave contact scales with the number of closed-channel molecules.

$p$-wave contact depends on short-range interaction details.

Abstract

We investigate universal relations in a spinless Fermi gas near a $p$-wave Feshbach resonance. We show that the momentum distribution $n_{\vec{k}}$ has an asymptote proportional to $k^{-2}$ with the proportionality constant--the $p$-wave contact-- scaling with the number of closed-channel molecules. We prove the adiabatic sweep theorem for a $p$-wave resonance which reveals the physical meaning of the $p$-wave contact in thermodynamics. In contrast to the unitary Fermi gas in which Tan's contact is universal, the $p$-wave contact depends on the short-range details of the interaction.