Rapidly rotating Bose-Einstein condensates in homogeneous traps

We extend the results of a previous paper on the Gross-Pitaevskii description of rotating Bose-Einstein condensates in two-dimensional traps to confining potentials of the form V(r)=rs, 2<∞. Writing the coupling constant as 1/ε2, we study the limit ε→0. We derive rigorously the leading asymptotics of the ground state energy and the density profile when the rotation velocity Ω tends to infinity as a power of 1/ε. The case of asymptotically homogeneous potentials is also discussed. © 2007 American Institute of Physics.