Inclusive spectra and Bose-Einstein correlations in small thermal quantum systems.

The spectra and correlation of identical particles emitted from small locally equilibrium sources are considered. The size of the system is defined by negative part of 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 when the size of the system is comparable to the thermal wave-length of the particles, the spectra and correlation functions are far from the quasi-classical approximation expecting for large systems, and observed femtoscopy scales (interferometry radii) will be essentially smaller than the Gaussian radii of the source. If the maximal value of chemical potential is closing to the critical one, specific for the system, one can consider a possibility of the Bose-Einstein condensation. Then the reduction of the intercept of the correlation function for inclusive measurements takes place. The results can be used for searching of femtoscopy homogeneity lengths in proton-proton collisions at the LHC energies.