In the first part of the talk I will review some of the results known for weakly interacting
bosons in box shaped and harmonic traps. Many results can be concluded from heuristic
and dimensional arguments [1]. In the second part this approach will be extended to
interacting bosons in a potential consisting of a superposition of a harmonic and a
random potential. New results for the size, shape and excitation energy of the condensate
as a function of the disorder strength and interaction are found using a semi-quantitative
analysis. For positive scattering length and sufficiently strong disorder the condensate
decays into fragments each of the size of the Larkin length. This state is stable over
a large range of particle numbers. For negative scattering length a condensate of size
of the Larkin length may exist as a metastable state. These findings are generalized to
anisotropic traps[2].
[1] T. Nattermann, Am. J. Phys. 73, 349(2005), 75, 938(2007).
[2] T. Nattermann and V.L. Pokrovsky, Bose-Einstein Condensates
in Strongly Disordered Taps arXiv: 0707.4444