A low-energy effective Hamiltonian for Landau quasiparticles: II Application to the contact Fermi gas

Abstract

This article follows up on arxiv:2511.15938, in which we developed a new renormalization scheme to construct a quantized theory of Fermi liquids. Here, we apply this formalism to a low-temperature atomic Fermi gas where the short-range interactions are fully parametrized by the s-wave scattering length $a$. We benchmark our renormalized theory by recovering known perturbative results on the static properties of the Fermi gas, such as the Lee-Huang-Yang expansion of the equation of state, the Galitskii expansion of the momentum distribution, and the Gor'kov- Melik Barkhudarov preexponential correction to the critical temperature. We then turn to the transport dynamics and demonstrate the presence of a preexponential correction to the speed of zero sound when including corrections of second order in $a$. Finally, we develop an efficient numerical method to solve the transport equation exactly, and we apply to study the crossover from the collisionless to the hydrodynamic regime in the density and polarisation response functions.