Quantum localization corrections from the Bethe-Salpeter equation

We investigate coherent matter wave transport in isotropic 3D speckle potentials by using the Bethe-Salpeter equation and the self-consistent theory of localization. This model constitutes an efficient tool to properly evaluate corrections to Boltzmann diffusion by taking into consideration quantum interference terms between the multiple-scattering paths. We calculate analytically and numerically the static current density, the density of states, the dipolar contribution and the reduced diffusion coefficient. Our results reveal that quantum corrections to diffusive transport, known as weak localization may not only lead to shift the above quantities but affect also the position of the mobility edge.