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We study quantum transport in anisotropic 3D disorder and show that nonrotation invariant correlations can induce rich diffusion and localizationproperties. For instance, structured finite-range correlations can lead to theinversion of the transport anisotropy. Moreover, working beyond theself-consistent theory of localization, we include the disorder-induced shiftof the energy states and show that it strongly affects the mobility edge.Implications to recent experiments are discussed.

Matter Wave Transport and Anderson Localization in Anisotropic 3D Disorder