The shape of the one-body density matrix (1.45) has been
calculated within the Bogoliubov model and is given by
(1.47) in the pure system and by (2.24) in the system
with disorder. The derivation of these results is valid
for dilute systems in the presence of weak
disorder, so one expects to find agreement with the DMC
results for small values of and .
Since the Bogoliubov model neglects short-range correlation, we
also expect that result (2.24) is valid for large values
of (, ).
The DMC simulation gives the mixed estimator for the OBDM and the
VMC gives the
variational estimate. By calculating these results using the
extrapolation technique (3.91),
we can estimate the pure OBDM.
We have calculated the OBDM at different densities and for a
fixed strength of the disorder . The results are shown in
Fig. 4.9. Although the strength of the disorder is
large we find good agreement at small densities while by increasing
in the density we see significant differences.
Figure 4.9:
One-body density matrix
at different
densities
,
and
with .
Solid lines correspond to result (2.24).