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Effective mass and normal fraction
If a quadratic term in the impurity contribution to the energy is present.
It can be denoted as
with
|
(7.19) |
being the induced mass, i. e. the mass of particles dragged by an impurity
[Ast01]. Applicability of the perturbation theory demands to be small
compared to This gives the condition
. At zero temperature the interaction between particles does not lead to depletion
of the superfluid density and the suppression of the superfluidity comes only from
the interaction of particles with impurities. Thus
defines the normal density
|
|
|
(7.20) |
This result is in agreement with the one obtained by the means of Bogoliubov
transformation starting from the Hamiltonian written in the second-quantized form in
the presence of disorder[HM92,ABCG02]. The normal density of a superfluid
is an observable quantity. It was evaluated in liquid He by measuring of the
moment of inertia of a rotating liquid or by measuring of the second sound velocity.
Both methods can be, in principle, developed for BEC gases.
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G.E. Astrakharchik
15-th of December 2004