Dimensionality and Finite Number Effect on BCS Transition of Atomic Fermi Gas

The effect of finite number and dimensionality has been discussed in thispaper. The finite number effect has a negative correction to final temperature for 2D or 3D atomicFermi gases. The changing of final temperature obtained by scanning from BEC region to BCS regionare 10% or so with N ≤ 10~3 and can be negligible when N 】 10~3. However, in ID atomic Fermi gas,the effect gives a positive correction which greatly changes the final temperature in Fermi gas.This behavior is completely opposed to the 2D and 3D cases and a proper explanation is still to befound. Dimensionality also has a positive correction, in which the more tightly trapping, the higherfinal temperature one gets with the same particle number. A discussion is also presented.