Abstract
We apply the Hartree-Fock-Bogoliubov-Popov (HFBP) method to two problems. The first is the phenomenon of Anderson localisation of a BEC in a two-dimensional bichromatic lattice. The second is the case of a harmonically trapped BEC with anisotropic, long-range, dipolar interactions between particles. The HFBP method allows us to calculate the condensate properties and excitation spectrum of the system at finite temperature. For the bichromatic lattice, we examine the effects of interactions and finite temperature on the the localisation of the condensate. We also include a synthetic magnetic field and determine its effect. For the dipolar BEC, we examine the effect of the dipolar interactions on the condensate and thermal cloud as well as the excitation spectrum of the system. At finite temperature, we calculate the effects of both direct and exchange dipolar interactions of the thermal cloud on the condensate. The exchange interactions are numerically intensive to calculate and have been excluded from most previous studies.