Finite-size effects on the cluster expansions for quantum gases in restricted geometries

Abstract

We have analytically obtained 1-particle density matrices for ideal Bose and Fermi gases in both the 3-D box geometries and the harmonically trapped geometries for the entire range of temperature. We have obtained quantum cluster expansions of the grand free energies in closed forms for the same systems in the restricted geometries. We have thoeremed (with a proof) about the generic form of the quantum cluster integral. We also have considered short ranged interactions in our analyses for the quasi 1-D cases of Bose and Fermi gases in the box geometries. Our theoretical results are exact, and are directly useful for understanding finite-size effects on quantum cluster expansion of Bose and Fermi gases in the restricted geometries. Our results would be relevant in the context of experimental study of spatial correlations in ultra-cold systems of dilute Bose and Fermi gases of alkali atoms (i) in 3-D magneto-optical box traps with quasi-uniform potential around the center [], and (ii) in 3-D harmonic traps [, ].

Artificial magnetism for a harmonically trapped Fermi gas in a synthetic magnetic field

“…Taylor expansion of the above logarithm about e µ/kBT = 0 and successive evaluation of the above summations, results in [32]…”

“…The average total number of particles (N = − ∂Φ ∂µ | T , ω ⊥ ,ωz,ΩB ) in the system can be obtained from equation (4), as [32]…”

Particle scattering by rotating trapped quantum gases at finite temperature

“…The scaling parameter is the same for both the length scales (l ⊥ and l z ) because the inter-scatterer interactions are isotropic. Further substantial change of the condensation point arises due to the finite-size effect [55,56].…”