Quasi-one-dimensional equation for a tube-shaped dilute Fermi gas

In this paper we consider a degenerate Fermi gas strongly confined in the transverse direction by a singular potential. By using an appropriate factorized ansatz from the three-dimensional mean-field model (i.e., a nonlinear Schrödinger equation) and using a variational approximation, we derive a one-dimensional (1D) effective equation that correctly describes the behavior of the particle distribution in the longitudinal direction. Systematic simulations are performed in view to confirm the robustness of the effective equation in describing the axial behavior of the tube-shaped Fermi gas in the attractive and repulsive regimes. Furthermore, from a dynamic point of view, we have analyzed the periodic oscillations of the wave function by abruptly increasing the depth of the harmonic axial potential, where we find that the 1D effective equation derived here is the best approximation to describe this oscillatory behavior.