Critical temperature for Bose-Einstein condensation in quartic potentials

The quartic confining potential has emerged as a key ingredient to obtain fast rotating vortices in BEC as well as observation of quantum phase transitions in optical lattices. We calculate the critical temperature T-c of bosons at which normal to BEC transition occurs for the quartic confining potential. Further more, we evaluate the effect of finite particle number on T-c and find that Delta T-c/T-c is larger in quartic potential as compared to quadratic potential for number of particles <10(5). Interestingly, the situation is reversed if the number of particles is greater than or similar to 10(5).