论文标题
耦合顶模型中的混乱和量子疤痕
Chaos and quantum scars in a coupled top model
论文作者
论文摘要
我们考虑了一个耦合的顶部模型，描述了两个相互作用的大型旋转，该自旋在半经典和量子上进行了研究。该模型表现出多种有趣的现象，例如量子相变（QPT），动力转变和激发状态量子相变，高于临界耦合强度。经典的动力学和纠缠熵都揭示了能量密度带的奇异行为，其中间耦合强度的中间范围高于QPT，其中水平间距分布从Poissonian到Wigner-Dyson统计量。有趣的是，在这种模型中，我们将量子疤痕识别为即使在存在相互作用的情况下，量子疤痕也是不稳定的集体动力学的回忆。这种疤痕状态的统计特性偏离了与随机矩阵理论相对应的沿着千古极限，并违反了贝瑞的猜想。与沿阵行的进化相反，在不等时间换向因素和生存概率的动力学中的振荡行为被视为量子疤痕的动态特征，这可能与其检测有关。
We consider a coupled top model describing two interacting large spins, which is studied semiclassically as well as quantum mechanically. This model exhibits variety of interesting phenomena such as quantum phase transition (QPT), dynamical transition and excited state quantum phase transitions above a critical coupling strength. Both classical dynamics and entanglement entropy reveals ergodic behavior at the center of energy density band for an intermediate range of coupling strength above QPT, where the level spacing distribution changes from Poissonian to Wigner-Dyson statistics. Interestingly, in this model we identify quantum scars as reminiscence of unstable collective dynamics even in presence of interaction. Statistical properties of such scarred states deviate from ergodic limit corresponding to random matrix theory and violate Berry's conjecture. In contrast to ergodic evolution, oscillatory behavior in dynamics of unequal time commutator and survival probability is observed as dynamical signature of quantum scar, which can be relevant for its detection.
