Effect of boundary conditions on fluctuations of the Bose condensate of interacting atoms

For a gas of trapped interacting atoms forming a Bose condensate, we demonstrate a possibility of a significant influence of the boundary conditions on the statistics of the number of particles in the fundamental mode of the system. The analysis is carried out in the Bogoliubov – Popov low-temperature approximation for model homogeneous cubic traps with periodic or combined periodic and zero boundary conditions. It is shown that the effect of the boundary conditions does not weaken even in the region of parameters corresponding to the relatively strong interaction in the Thomas – Fermi asymptotic case, and does not disappear when proceeding to the thermodynamic limit. (paper)