Abstract
Abstract We investigate the finite temperature properties with replica approach to deal with generalized disorder type. After averaging out the disorder, we get the effective Lagrange in which the disorder acts like two-particle potential. Then, to cope with such potential and the interaction term, we introduce Hubbard-Stratonovich transformation and obtain the equation of states. We present an analytical solution in the case of the uniform system as an example, showing how random potential can deplete the condensate particles and change the properties of elementary excitations.