BOSE-EINSTEIN CONDENSATION OF A FINITE NUMBER OF PARTICLES TRAPPED INONE OR 3 DIMENSIONS

Bose-Einstein condensation (BEC) of an ideal gas is investigated for a finite number of particles. In three dimensions, we find a transition temperature which is lower than in the thermodynamic limit. Lowering the dimension increases the transition temperature and is therefore fa vorable for BEG. This is in contrast to the standard result obtained i n the thermodynamic limit which states that BEC is not possible in, e. g., a one-dimensional (1D) harmonic potential. As a result, 1D atom tr aps, such as radially tightly confining magnetic traps or optical dipo le traps, are promising fdr studying BEC.