van Zyl, Brandon P. and Bhaduri, Rajat K. and Suzuki, Akira and Brack, Matthias (2003) Some exact results for a trapped quantum gas at finite temperature. PHYSICAL REVIEW A, 67 (2): 023609. ISSN 1050-2947
Full text not available from this repository.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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | KINETIC-ENERGY DENSITIES; NONINTERACTING FERMIONS; HARMONIC TRAP; PARTICLE; BOSE; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Alumni or Retired Professors > Group Matthias Brack |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 24 Aug 2021 13:02 |
| Last Modified: | 24 Aug 2021 13:02 |
| URI: | https://pred.uni-regensburg.de/id/eprint/39329 |
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