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 phase of each of the two condensates doesn't remain random at the Boltzmann equilibrium, but is distributed around integer multiple values of $2\pi$ from the interference and thermalization of forward and backward propagating matter waves. The thermalization inside the atomic vapors can be understood as an intrinsic measurement process that defines a temperature for the two condensates and projects the quantum states to an average wave field with zero (relative) phases. Following this approach, focus is put on the original thought 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被相干耦合的情况进行了数值实验。本模型从头计算表明：在玻尔兹曼平衡态下，两个凝聚体各自的初始相位并不会保持随机分布，而是会因前向与反向传播物质波的干涉和热化作用，围绕$2\pi$的整数倍值分布。原子蒸气内部的热化可被理解为一个本征的测量过程，该过程为两个凝聚体定义了温度，并将量子态投影至具有零（相对）相位的平均波场。基于这一思路，我们重点关注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出现，取决于初始相位分布。