In this chapter we discuss the theory of a dilute Bose gas in the
presence of disorder.
Within the Bogoliubov model we study the effects of a weak external
random potential, which is modeled by a uniform random distribution
of quenched impurities. We calculate the corrections to the ground
state energy and to the condensate fraction due to the external
random potential. We also investigate the behavior of the one-body
density matrix.
The second part of this chapter is devoted to the microscopic
definition of the superfluid density. By using the
Bogoliubov model we study the effect of the external
field on the superfluid density. This result is also obtained in
a new alternative way which makes use of the Gross-Pitaevskii equation.
