论文标题
量子系统中的规模纠缠产生模拟经典混乱的量子系统
Interscale entanglement production in a quantum system simulating classical chaos
论文作者
论文摘要
这是一个基本问题，如何从量子力学的微观描述中出现古典混乱的普遍概念。我们在这里研究量子力学框架中的标准古典混乱。特别是，我们设计了一个量子晶格系统，该系统在适当的连续体极限后精确模拟了经典的混乱，这称为“汉密尔顿方程极限”。我们分析的关键概念是通过将晶格分为相等大小的许多块并追踪每个区块内的自由度来定义的纠缠熵。我们将此熵称为“范围内熵”，因为它测量了每个块内部自由度之间的纠缠量与定义波函数大规模结构的宏观自由度。通过数值模拟与踢旋翼的哈密致力的量子晶格系统，我们发现，只有当混乱在哈密顿方程式限制中出现时，尺度间纠缠熵的长时间平均值才能积极，并且熵的增长率与初始阶段的熵速率与相应的分类系统的粗grogred gibbs熵熵成比例。
It is a fundamental problem how the universal concept of classical chaos emerges from the microscopic description of quantum mechanics. We here study standard classical chaos in a framework of quantum mechanics. In particular, we design a quantum lattice system that exactly simulates classical chaos after an appropriate continuum limit, which is called the "Hamiltonian equation limit". The key concept of our analysis is an entanglement entropy defined by dividing the lattice into many blocks of equal size and tracing out the degrees of freedom within each block. We refer to this entropy as the "interscale entanglement entropy" because it measures the amount of entanglement between the microscopic degrees of freedom within each block and the macroscopic degrees of freedom that define the large-scale structure of the wavefunction. By numerically simulating a quantum lattice system corresponding to the Hamiltonian of the kicked rotor, we find that the long-time average of the interscale entanglement entropy becomes positive only when chaos emerges in the Hamiltonian equation limit, and the growth rate of the entropy in the initial stage is proportional to that of the coarse-grained Gibbs entropy of the corresponding classical system.
