Hydrodynamic excitations in a spin-polarized Fermi gas under harmonic confinement in one dimension - art. no. 033605

We consider a time-dependent nonlinear Schrodinger equation in one dimensio n (1D) with a fifth-order interaction term and external harmonic confinemen t, as a model for both (i) a Bose gas with hard-core contact interactions i n the local-density approximation, and (ii) a spin-polarized Fermi gas in t he collisional regime. We evaluate analytically in the Thomas-Fermi limit t he density fluctuation profiles and the collective excitation frequencies, and compare the results for the low-lying modes with those obtained from nu merical solution of the Schrodinger equation. We find that the excitation f requencies are multiples of the harmonic-trap frequency even in the strong- coupling Thomas-Fermi regime. This result shows that the hydrodynamic and t he collisionless collective spectra coincide in the harmonically confined 1 D Fermi gas, as they do for sound waves in its homogeneous analog. It also shows that in this case the local-density theory reproduces the exact colle ctive spectrum of the hard-core Bose gas under harmonic confinement.