  The spectra and correlation of identical particles emitted from small
local-equilibrium sources are considered. The size of the system is defined by
the negative part of the parabolic falling chemical potential. The analytical
solution of the problem is found for the case of inclusive measurements. It is
shown that in the case where the size of the system is comparable to the
thermal wavelength of the particles, the spectra and correlation functions are
far from the quasiclassical approximation expected for large systems, and
observed femtoscopy scales (interferometry radii) will be essentially smaller
than the Gaussian radii of the source. If the maximum value of the chemical
potential approaches the critical one, specific for the system, one can
consider the possibility of the Bose-Einstein condensation. In such a case the
reduction of the intercept of the correlation function for inclusive
measurements takes place. The results can be used for the searching of
femtoscopy homogeneity lengths in proton-proton collisions at LHC energies.
