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 σR. For speckle potentials the Fourier transform of the correlation function vanishes for momenta k>2/σR so that the Lyapunov exponent vanishes in the Born approximation for k>1/σR. Then, for the initial healing length of the condensate ξᵢₙ>σR the localization is exponential, and for ξᵢₙ<σR it changes to algebraic.
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Sanchez-Palencia et al. (2007) studied this question.
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