Anderson localization of expanding Bose-Einstein condensates in random potentials

We show that the expansion of an initially confined interacting 1D Bose-Einstein condensate can exhibit Anderson localization in a weak random potential with correlation length sigma(R). For speckle potentials the Fourier transform of the correlation function vanishes for momenta k > 2/sigma(R) so that the Lyapunov exponent vanishes in the Born approximation for k > 1/sigma(R). Then, for the initial healing length of the condensate xi(in)>sigma(R) the localization is exponential, and for xi(in)