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Superfluidity and Bose-Einstein condensation in a dipolar Bose gas with weak disorder

We investigate the properties of a three-dimensional homogeneous dipolar Bose gas in a weak random potential with a Gaussian correlation function at finite temperature. Using the Bogoliubov theory (beyond the mean field), we calculate the superfluid and the condensate fractions in terms of the interaction strength on the one hand and in terms of the width and the strength of the disorder on the other. The influence of the disordered potential on the second order correlation function, the ground state energy and the chemical potential is also analyzed. We find that for fixed strength and correlation length of the disorder potential, the dipole-dipole interaction leads to modify both the condensate and the superfluid fractions. We show that for a strong disorder strength the condensed fraction becomes larger than the superfluid fraction. We discuss the effect of the trapping potential on a disordered dipolar Bose in the regime of large number of particles.