Functional Integral Approach to Disordered Bosons

The appearance of coherence and order is studied for ultracold bosonic atoms in the presence of additional disorder potentials. These arise either naturally like in current carrying wire traps, or artificially and controllably like in laser speckle fields. The description of such disordered bosons within a suitably generalized Bogoliubov theory, first given by Huang and Meng, is rederived here within a functional integral approach for replicated bosonic fields. The superfluidity in homogeneous Bose systems with condensates depleted by weak interactions and disorder can thereby be discussed.