Bose-Einstein condensates in strongly disordered traps

A Bose-Einstein condensate in an external potential consisting of a superposition of a harmonic and a random potential is considered theoretically. From a semiquantitative analysis we find the size, shape, and excitation energy as a function of the disorder strength. For positive scattering length and sufficiently strong disorder the condensate decays into fragments each of the size of the Larkin length L. This state is stable over a large range of particle numbers. The frequency of the breathing mode scales as 1/L-2. For negative scattering length a condensate of size L may exist as a metastable state. These findings are generalized to anisotropic traps.