Partition Function of the Bose-Einstein Condensed Dark Matter and the
  Modified Gross-Pitaevskii Equation
  Intending to describe the dark matter of dwarf galaxies, we concentrate on
one model of the slowly rotating and gravitating Bose-Einstein condensate. For
a deeper understanding of its properties, we calculate the partition function
and compare the characteristics derived from it with the results based on the
solution of Gross-Pitaevskii equation. In our approach, which uses the Green's
functions of spatial evolution operators, we formulate in a unified way the
boundary conditions, important for applying the Thomas-Fermi approximation.
Taking this into account, we revise some of the results obtained earlier. We
also derive the spatial particle distribution, similar to the model with
rotation, by using the deformation of commutation relations for a macroscopic
wave function and modifying the Gross-Pitaevskii equation. It is shown that
such an approach leads to the entropy inhomogeneity and makes the distribution
dependent on temperature.
