Finite-Size Effects Within The 2D BEC-BCS Crossover
We study the finite size effects within the 2D Bose-Einstein-Condensate (BEC) Bardeen-Cooper-Schrieffer(BCS) crossover by varying particle number from small to large to determine the effect on the pairing gap via ground state Diffusion-Monte- Carlo (DMC) calculations. Progress is made in the determination of a 2D mean field gap calculation and the 2D gap expression as well as a potential V(k, k') is derived. Using a two body attractive Poschl-Teller potential and 10 optimization parameters we determine optimized wavefunctions with energy minimization. We then vary the number of particle around closed shell values N=10,18,26,42,50,58 and use prescribed methods to determine the pairing gap through out the crossover region with coupling eta = 0.5 to eta = 3.0. We see predicted energy pairing gap suppression from the mean field line in the BCS limit not seen in previous DMC calculations. These results provide a detailed look at the finite size effects present within the BEC-BCS crossover region and show the sensitivity of the gap to finite size effects.