The strength of disorder is described by two independent
parameters: the particle-impurity scattering length
and the concentration
. One
of the important results of the Bogoliubov model is that a
single parameter
is sufficient to describe the
effect of disorder (see eqs. (2.17),
(2.22), (2.65)).
We have calculated the condensate and superfluid fraction by
changing both and while keeping
constant. The results are shown in Fig. 4.7 for
and and in Fig. 4.8 for
and .
Figure 4.7:
Condensate fraction and superfluid fraction
as functions of impurity size for two values of the scaling
parameter and , and density
Figure 4.8:
Condensate fraction and superfluid fraction
as functions of impurity size for fixed value of the scaling
parameter and , and density
Both at low and high density we see that the scaling behavior for
and is well satisfied for the smallest values
of ( for and for ).
It is worth noticing that these values of and
correspond to regime where the results of first order perturbation
theory do not apply (see Figs. 4.5, 4.6).
This means that the scaling behavior in the parameter is valid
also beyond the region of applicability of the perturbation
expansion.
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