The Bogoliubov c-Number Approximation for Random Boson Systems

We justify the Bogoliubov c-number approximation for the case of interacting Bose-gas in a homogeneous random media. To this aim we take into account occurrence of generalised extended/fragmented Bose-Einstein condensation in an infinitesimal band of low kinetic-energy modes, to generalise the c-number substitution procedure for this band of low-momenta modes.