A numerical experiment based on a particle number-conserving quantum field theory is performed for two initially independent Bose-Einstein condensates that are coherently coupled at two temperatures. The present model illustrates ab initio that the initial relative phase of each of the two condensates doesn't remain random, but is distributed around integer multiple values of $2\pi$ from the interference and thermalization of forward and backward propagating matter waves at the Boltzmann equilibrium, that intrinsically measures zero average phases for each of the two independent condensates. Following this approach, focus is put on the original Gedanken experiment of Anderson on whether a Josephson current between two initially separated Bose-Einstein condensates occurs in a deterministic way or not, depending on the initial phase distribution.

翻译：基于粒子数守恒的量子场论，我们对两个初始独立的玻色-爱因斯坦凝聚体在两种温度下进行相干耦合的数值实验。本模型从头计算表明：在玻尔兹曼平衡态下，由于前向与反向传播物质波的干涉和热化作用，两个凝聚体各自的初始相对相位并非保持随机分布，而是围绕$2\pi$的整数倍值分布；这本质上意味着两个独立凝聚体的平均相位皆为零。基于此方法，我们聚焦于安德森提出的原始思想实验：两个初始分离的玻色-爱因斯坦凝聚体间的约瑟夫森电流是否以确定性的方式发生，取决于初始相位分布。