2001/06/01 by A. Minguzzi, Anna Minguzzi, P. Vignolo +3
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Excitation #Fermi Gamma-ray Space Telescope #Fermi gas #Harmonic #Physics #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #Quasiparticle #Spin (aerodynamics) #Strong Light-Matter Interactions #cond-mat
paper · pdf · doi:10.1103/physreva.64.033605
published as Phys. Rev. A 64, 033605 (2001) · 7 pages, 3 figures, to appear on Phys. Rev. A
arxiv created 2001/06/01 · openalex publication_date 2001/08/13 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider a time-dependent nonlinear Schr"odinger equation in one dimension (1D) with a fifth-order interaction term and external harmonic confinement, as a model for both (i) a Bose gas with hard-core contact interactions in the local-density approximation, and (ii) a spin-polarized Fermi gas in the collisional regime. We evaluate analytically in the Thomas-Fermi limit the density fluctuation profiles and the collective excitation frequencies, and compare the results for the low-lying modes with those obtained from numerical solution of the Schr"odinger equation. We find that the excitation frequencies are multiples of the harmonic-trap frequency even in the strong-coupling Thomas-Fermi regime. This result shows that the hydrodynamic and the collisionless collective spectra coincide in the harmonically confined 1D 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 collective spectrum of the hard-core Bose gas under harmonic confinement.