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.

中文翻译：

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边界条件对相互作用原子的玻色子凝聚物涨落的影响

对于形成Bose冷凝物的被捕获的相互作用原子的气体，我们证明了在系统基本模式下边界条件对粒子数量统计的重大影响的可能性。该分析是在Bogoliubov – Popov低温近似方法中对具有周期边界条件或周期边界条件和零边界条件的均相立方阱模型进行的。结果表明，即使在与托马斯-费米渐近情况下相对较强的相互作用相对应的参数范围内，边界条件的影响也不会减弱，并且在进行热力学极限时不会消失。