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This article studies multiple scattering of matter waves by a disorderedoptical potential in two and in three dimensions. We calculate fundamentaltransport quantities such as the scattering mean free path $\ell_s$, theBoltzmann transport mean free path $\elltrb$, and the Boltzmann diffusionconstant $D_B$, using a diagrammatic Green functions approach. Coherentmultiple scattering induces interference corrections known as weak localizationwhich entail a reduced diffusion constant. We derive the correspondingexpressions for matter wave transport in an correlated speckle potential andprovide the relevant parameter values for a possible experimental study of thiscoherent transport regime, including the critical crossover to the regime ofstrong or Anderson localization.Comment: 33 pages, minor corrections, published versio

Coherent matter wave transport in speckle potentials