  By improving the Bose-Einstein condensate model of dark matter through the
repulsive three-particle interaction to better reproduce observables such as
rotation curves, both different thermodynamic phases and few-particle
correlations are revealed. Using the numerically found solutions of the
Gross-Pitaevskii equation for averaging the products of local densities and for
calculating thermodynamic functions at zero temperature, it is shown that the
few-particle correlations imply a first-order phase transition and are reduced
to the product of single-particle averages with a simultaneous increase in
pressure, density, and quantum fluctuations. Under given conditions, dark
matter exhibits rather the properties of an ideal gas with an effective
temperature determined by quantum fluctuations. Characteristics of oscillations
between bound and unbound states of three particles are estimated within a
simple random walk approach to qualitatively models the instability of particle
complexes. On the other hand, the density-dependent conditions for the
formation of composites are analyzed using chemical kinetics without specifying
the bonds formed. The obtain results can be extended to the models of
multicomponent dark matter consisting of composites formed by particles with a
large scattering length.
