It is easy to obtain the particle momentum distribution
from the operator transformation (2.16).
(2.20)
where
is the number of excitations with momentum .
At zero temperature such excitations are absent and the distribution
(2.20) takes the form
(2.21)
The first term of the above result corresponds to the momentum
distribution in the absence of disorder. The second term gives the
contribution due to disorder. The presence of disorder induces an
extra quantum depletion of the condensate arising from the
particle-impurity interaction. By integrating over momentum one
obtains the following result for the condensate fraction