Universal High-Momentum Asymptote and Thermodynamic Relations in a Spinless Fermi Gas with a Resonant $p$-Wave Interaction

We investigate universal relations in a spinless Fermi gas near a $p$-wave Feshbach resonance, and show that the momentum distribution $n_{\mathit{k}}$ 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 thermodynamic implication of the $p$-wave contact. 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.