Analytical treatment of interacting Fermi gas in arbitrary dimensional harmonic trap
arXiv:cond-mat/0210198 · doi:10.1088/0305-4470/36/42/004
Abstract
We study normal state properties of an interacting Fermi gas in an isotropic harmonic trap of arbitrary dimensions. We exactly calculate the first-order perturbation terms in the ground state energy and chemical potential, and obtain simple analytic expressions of the total energy and chemical potential. At zero temperature, we find that Thomas-Fermi approximation agrees well with exact results for any dimension even though system is dilute and small, i.e. when the Thomas-Fermi approximation is generally expected to fail. In the high temperature (classical) region, we find interaction energy decreases in proportion to T^(-d/2), where T is temperature and d is dimension of the system. Effect of interaction in the ground state in two and three-dimensional systems is also discussed.
15 pages, 4 figures
References in corpus (17)
- The BCS-BEC Crossover in a Gas of Fermi Atoms with a Feshbach Resonance
- Superfluidity of spin-polarized 6Li
- Self-consistent model of ultracold atomic collisions and Feshbach resonances in tight harmonic traps
- Elastic and inelastic collisions of 6Li in magnetic and optical traps
- BCS Theory for Trapped Ultracold Fermions
- Sympathetic cooling of bosonic and fermionic Lithium gases towards quantum degeneracy
- Collective oscillations of an interacting trapped Fermi gas
- Signatures of resonance superfluidity in a quantum Fermi gas
- Stable, Strongly Attractive, Two-State Mixture of Lithium Fermions in an Optical Trap
- Cooper pairing and single particle properties of trapped Fermi gases
- Some exact results for a trapped quantum gas at finite temperature
- Fractional Exclusion Statistics and Two Dimensional Electron Systems
- Exclusion Statistics in a trapped two-dimensional Bose gas
- Luttinger model approach to interacting one-dimensional fermions in a harmonic trap
- Two-component Fermi gas in a one-dimensional harmonic trap
- Manipulating the critical temperature for the superfluid phase transition in trapped atomic Fermi gases
- Exclusion Statistics in a two-dimensional trapped Bose gas