Another interesting result that can be obtained from Bogoliubov
theory is the momentum distribution of the particles. The number of
particles with momentum is given by
or using the transformation (1.32) it is given by
(1.41)
here
is the number of elementary excitations,
which satisfy the usual Bose distribution
.
At zero temperature such excitations are absent and (1.41) simplifies to
(1.42)
As the momentum distribution diverges as .
The number of atoms in the condensate can be obtained by taking
the difference between and the number of non-condensed atoms.
(1.43)
The integration can be carried out and gives the result
(1.44)
Due to interactions particles are pushed out of the condensate and
a fraction of particles with nonzero momenta is present even at
zero temperature. This phenomenon is called
quantum depletion of the condensate
Also result (1.44) is valid in the dilute regime
in which the quantum depletion is small and Bogoliubov
theory applies.
Next:One-body density matrix Up:Beyond mean-field: Bogoliubov theory Previous:Ground state energy
  Contents