Hyperspherical Description of the Degenerate Fermi Gas: S-wave Interactions

Abstract

We present a unique theoretical description of the physics of the spherically trapped $N$-atom degenerate Fermi gas (DFG) at zero temperature based on an ordinary Schrödinger equation with a microscopic, two body interaction potential. With a careful choice of coordinates and a variational wavefunction, the many body Schrödinger equation can be accurately described by a \emph{linear}, one dimensional effective Schrödinger equation in a single collective coordinate, the rms radius of the gas. Comparisons of the energy, rms radius and peak density of ground state energy are made to those predicted by Hartree-Fock (HF). Also the lowest radial excitation frequency (the breathing mode frequency) agrees with a sum rule calculation, but deviates from a HF prediction.

References in corpus (2)

• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Stability of trapped fermionic gases with attractive interactions

Cited by in corpus (5)

• Energetics and Structural Properties of Trapped Two-Component Fermi Gases
• Stability of Inhomogeneous Multi-Component Fermi Gases
• Few-body collective excitations beyond Kohn's theorem in quantum Hall systems
• Orbital Variational Adiabatic Hyperspherical Method Applied to Bose-Einstein Condensates
• Hyperspherical approach to dipolar Bose-Einstein condensates beyond the mean-field limit