We have studied the dynamics of a two-site Bose–Einstein condensate subject to tunnelling coupling (which makes the system a bosonic Josephson junction), having on-site inter-particle interaction (making the system a small Bose–Hubbard model) and in contact with two separate heat baths, which makes the system lossy and potentially drives it into a non-equilibrium state with some heat current. The dynamical calculation of the system is done within the standard quantum generalized Langevin setting, and the heat baths are assumed to have non-zero memory time (Ornstein–Uhlenbeck process). We numerically calculated the time evolution of the population imbalance, coherence and entanglement of the system. We have shown inter-particle interaction, noise and dissipation induced by BEC atoms-reservoir interaction that are crucial in affecting the dynamics of the mentioned physical parameters. The study also indicates that quantumness (non-classicality) of the system is characterized by the interplay between dissipation and inter-particle interaction.

我们研究了受隧穿耦合（使系统成为玻色约瑟夫森结）、具有现场粒子间相互作用（使系统成为小型 Bose-Hubbard 模型）和在与两个独立的热浴接触，这会使系统有损并可能通过一些热流将其驱动到非平衡状态。系统的动力学计算是在标准量子广义朗之万设置内完成的，并且假定热浴具有非零记忆时间（Ornstein-Uhlenbeck 过程）。我们数值计算了系统人口失衡、连贯性和纠缠的时间演化。我们已经展示了粒子间的相互作用，BEC 原子-储层相互作用引起的噪声和耗散，这对于影响上述物理参数的动力学至关重要。该研究还表明，系统的量子性（非经典性）以耗散和粒子间相互作用之间的相互作用为特征。