Instability and Depletion of an Excited Bose-Einstein Condensate in a Trap

We present an analytical method to calculate the depletion of a Bose-Einstein condensate excited in a time dependent harmonic trap. We identify a regime where the motion of the condensate is unstable and show that this instability leads to an exponentially fast population of noncondensed modes. As these modes are concentrated on the surface of the condensate this is observable in the particle density.