Evolution of a Bose-Einstein condensate in a rapidly expanding circular box.

We examine the evolution of the ground state of a Bose-Einstein condensate in a two-dimensional circular box, the wall of which is initially at rest and then recedes with large and constant speed. The final state of the condensate depends on the rapidity of the expansion of the box. If the number of atoms in the condensate is small compared to the dimensionless speed of the wall, then the condensate becomes a mixture of excitations and follows the expansion of the box, leaving empty though an increasingly larger region between the condensate boundary and the wall. If, on the other hand, the number of atoms is large compared to the dimensionless speed of the wall, then the condensate is always in the ground state and spreads uniformly in all of the expanding box, the condensate boundary always coinciding with the receding wall. Approximate analytic expressions are found for the evolving wave function.