Macroscopic quantum tunneling of the Bose-Einstein condensate trapped in cylindrically symmetric potential

We investigate the macroscopic quantum tunneling of the attractive Bose-Einstein condensate. Within the effective Lagrangian framework, we find bounce solutions and explicitly calculate the decay rate of the condensate trapped in a cylindrically symmetric potential. In particular, in the case where the number of condensed bosons is slightly below a certain critical number, we present a detailed analysis of the bounce solutions and discuss the approximations employed in our calculations. The effects of finite temperatures and the shape of the trapping potential are evaluated.