Cylindrical Trap Dependence in the Unitary Fermi Gas

The unitary Fermi gas serves as a tunable realization of a strongly coupled CFT, making it a powerful system for probing universal quantum many-body phenomena. Precise measurement of its properties remains experimentally challenging: finite-temperature effects and spatial inhomogeneity introduced by external trapping potentials can significantly distort observables. Cylindrical trap geometries are commonly used in experiments. This note extends an existing theoretical framework to this geometry, deriving how the cylindrical confinement modifies the dynamic structure factor at zero temperature. These results provide a necessary correction for the interpretation of experimental spectra in trapped unitary gases.