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 > \sigma_R the localization is exponential, and for \xi < \sigma_R it changes to algebraic. 
Laurent Sanchez-Palencia (LCFIO), David Cl\'ement (LCFIO), Pierre   Lugan (LCFIO), Philippe Bouyer (LCFIO), Georgy V. Shlyap...