Oscillations of a Bose–Einstein condensate in a rapidly contracting circular box

A Bose–Einstein condensate will evolve almost adiabatically if the number of atoms is large enough, even though the trap parameters may be changing rapidly. We demonstrate this by examining a Bose–Einstein condensate in a two-dimensional rapidly contracting circular box. We show that as a result of the contraction the condensate will oscillate about the instantaneous ground state. These oscillations will be small though when the number of atoms is large. Approximate analytic expressions are found for the evolving condensate wavefunction, both before and after the contraction has begun.