Some exact results for a trapped quantum gas at finite temperature
arXiv:cond-mat/0209460 · doi:10.1103/PhysRevA.67.023609
Abstract
We present closed analytical expressions for the particle and kinetic energy spatial densities at finite temperatures for a system of noninteracting fermions (bosons) trapped in a d-dimensional harmonic oscillator potential. For d=2 and 3, exact expressions for the N-particle densities are used to calculate perturbatively the temperature dependence of the splittings of the energy levels in a given shell due to a very weak interparticle interaction in a dilute Fermi gas. In two dimensions, we obtain analytically the surprising result that the |l|-degeneracy in a harmonic oscillator shell is not lifted in the lowest order even when the exact, rather than the Thomas-Fermi expression for the particle density is used. We also demonstrate rigorously (in two dimensions) the reduction of the exact zero-temperature fermionic expressions to the Thomas-Fermi form in the large-N limit.
14 pages, 4 figures included
References in corpus (2)
Cited by in corpus (18)
- Coherence properties of the two-dimensional Bose-Einstein condensate
- Density profile of a harmonically trapped ideal Fermi gas in arbitrary dimension
- Exact first-order density matrix for a d-dimensional harmonically confined Fermi gas at finite temperature
- Airy-averaged gradient corrections for two-dimensional fermion gases
- Ideal Fermi gases in harmonic oscillator potential traps
- A nonlocal kinetic energy functional for an inhomogeneous two-dimensional Fermi gas
- Semiclassical theory for spatial density oscillations in fermionic systems
- Exact results for a charged, harmonically trapped quantum gas at arbitrary temperature and magnetic field strength
- Harmonically trapped jellium
- Gradient corrections to the kinetic energy density functional of a two-dimensional Fermi gas at finite temperature
- Exact coherent states of a noninteracting Fermi gas in a harmonic trap
- Analytical treatment of interacting Fermi gas in arbitrary dimensional harmonic trap
- Exact and asymptotic local virial theorems for finite fermionic systems
- Super-shell structures and pairing in ultracold trapped Fermi gases
- Finite temperature analytical results for a harmonically confined gas obeying exclusion statistics in -dimensions
- Expansion of a mesoscopic Fermi system from a harmonic trap
- On the spin asymmetry of ground states in trapped two-component Fermi gases with repulsive interactions
- Evaluation of inverse integral transforms for undergraduate physics students