We consider a model describing Bose-Josephson junction (BJJ) coupled to a single bosonic mode exhibiting quantum phase transition (QPT). Onset of chaos above QPT is observed from semiclassical dynamics as well from spectral statistics. Based on entanglement entropy, we analyze the ergodic behavior of eigenstates with increasing energy density which also reveals the influence of dynamical steady state known as $\pi$-mode on it. We identify the imprint of unstable $\pi$-oscillation as many body quantum scar (MBQS), which leads to the deviation from ergodicity and quantify the degree of scarring. Persistence of phase coherence in nonequilibrium dynamics of such initial state corresponding to the $\pi$-mode is an observable signature of MBQS which has relevance in experiments on BJJ.

中文翻译：

---

玻色-约瑟夫逊结的耦合的玻色子模式中的混沌和量子疤痕

我们考虑一个模型，该模型描述Bose-Josephson结（BJJ）与展示量子相变（QPT）的单个玻色子模式耦合。从半经典动力学以及频谱统计中可以观察到QPT之上出现混乱。基于纠缠熵，我们分析了本征态随能量密度增加的遍历行为，这也揭示了动态稳态的影响，即$\pi$-模式就可以了。我们确定不稳定的烙印$\pi$-振动会导致人体量子疤痕（MBQS）增多，从而导致偏离遍历性并量化疤痕程度。在这种初始状态的非平衡动力学中，相位相干的持续性对应于$\pi$-mode是MBQS的一个可观察的特征，它与BJJ的实验有关。