Determination of Landau Fermi-liquid parameters of strongly interacting fermions by means of a nonlinear scaling transformation

A nonlinear transformation approach is formulated for the correlated fermions’ thermodynamics through a medium-scaling effective action. An auxiliary implicit variable-effective chemical potential is introduced to characterize the non-Gaussian fluctuations physics. By incorporating the nonlocal correlation effects, the achieved grand partition function is made of coupled highly nonlinear parametric equations. Analytically, the low temperature expansions for the strongly interacting unitary Fermi gas are performed for the adiabatic compressibility-sound speed and specific heat with the Sommerfeld lemma. The expressions for the Landau Fermi-Liquid parameters $F_0^s$ and $F_1^s$ of the strongly interacting fermion system are obtained. As a universal constant, the effective fermion mass ratio is $m^*/m={10/9}$ at unitarity.

💡 Research Summary

In this work the author develops a non‑perturbative statistical‑mechanical framework for the unitary (infinitely strongly interacting) Fermi gas by introducing a medium‑dependent effective action. The bare contact interaction (U_0=4\pi a/m) is replaced by a density‑ and temperature‑dependent effective coupling (U_{\text{eff}}