We analyze the Casimir forces for an ideal Bose gas enclosed between two infinite parallel walls separated by the distance D. The walls are characterized by the Dirichlet boundary conditions. We show that if the thermodynamic state with Bose-Einstein condensate present is correctly approached along the path pertinent to the Dirichlet b.c. then the leading term describing the large-distance decay of thermal Casimir force between the walls is 1/D^2 with a non-universal amplitude. The next order correction is lnD/D^3. These observations remain in contrast with the decay law for both the periodic and Neumann boundary conditions for which the leading term is 1/D^3 with a universal amplitude. We associate this discrepancy with the non-zero D-dependent positive value of the one-particle ground state energy in the case of Dirichlet boundary conditions.

中文翻译：

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接近理想气体玻色-爱因斯坦凝聚的非普遍卡西米尔力：狄利克雷边界条件的影响

我们分析了理想 Bose 气体的卡西米尔力，该气体被封闭在由距离 D 隔开的两个无限平行壁之间。壁的特征是狄利克雷边界条件。我们表明，如果沿着与狄利克雷 bc 相关的路径正确接近存在玻色 - 爱因斯坦凝聚的热力学状态，那么描述壁之间热卡西米尔力的大距离衰减的主要项是 1/D^2，非- 通用振幅。下一个顺序修正是 lnD/D^3。这些观察结果与周期和诺依曼边界条件的衰减定律形成对比，其主要项是具有普遍幅度的 1/D^3。在狄利克雷边界条件的情况下，我们将这种差异与单粒子基态能量的非零依赖于 D 的正值联系起来。