Dependence of the Bose-Condensate Population Fluctuations in a Gas of Interacting Particles on the System Size: Numerical Analysis

We consider the Bose-condensate population statistics for a gas of interacting particles confined into a three-dimensional cubic trap with different boundary conditions at a low temperature. Behavior of the mathematical expectation and variance of the condensate population with the system size increase corresponding to the transition to a thermodynamic limit at constant temperature and density of the gas is examined on the basis of numerical calculations. A competition between the thermal and quantum contributions to the moments of the statistical distribution, as well as the dependence of the statistics character on the boundary conditions, are analyzed for a wide range of trap sizes corresponding to the actual experiments. We estimate with what accuracy and starting with which system sizes the thermodynamic-limit results could be applied to the actual mesoscopic systems.