Interscale entanglement production in a quantum system simulating classical chaos
Interscale entanglement production in a quantum system simulating classical chaos
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模拟经典混沌的量子系统中的尺度间纠缠产生
DOI：
10.1088/1742-5468/aca2a1
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Taiki Haga and Shin-ich Sasa
中科院分区：
文献类型：
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作者：
Hiraizumi Mao;Ohta Hiroki;Sasa Shin-ichi;Taiki Haga and Shin-ich Sasa
经典混沌的普遍概念如何从量子力学的微观描述中产生是一个基本问题。我们在量子力学的框架下研究标准的经典混沌。特别地，我们设计了一个量子晶格系统，它在适当的连续极限（称为“哈密顿方程极限”）之后精确地模拟了经典混沌。我们分析的关键概念是纠缠熵，它是通过将晶格分成许多大小相等的块并追踪每个块内的自由度来定义的。我们将这种熵称为“尺度间纠缠熵（IEE熵）”，因为它测量了每个块内微观自由度与定义波函数大尺度结构的宏观自由度之间的纠缠量。通过数值模拟一个对应于被踢转子哈密顿量的量子晶格系统，发现IEE的长时间平均值只有在哈密顿方程极限出现混沌时才变为正值，初始阶段熵的增长率与对应经典系统的粗粒Gibbs熵的增长率成正比.
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 (IEE)'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 wave function. By numerically simulating a quantum lattice system corresponding to the Hamiltonian of the kicked rotor, we find that the long-time average of the IEE 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.