Breakdown of quantum-classical correspondence and dynamical generation of entanglement
Breakdown of quantum-classical correspondence and dynamical generation of entanglement
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DOI：
10.1103/physrevb.104.174302
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发表时间：
2021-04
影响因子：
3.7
通讯作者：
C. Tian;Kun Yang
中科院分区：
文献类型：
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作者：
C. Tian;Kun Yang
由粒子不可区分性引起的交换相互作用对于多粒子量子系统的物理学至关重要。在这里，我们分析研究了孤立系统中这种相互作用引起的量子纠缠的动态生成，即限制在混沌腔中的理想费米气体，它从非高斯纯态统一演化而来。我们发现，粒子运动的量子经典对应关系的破裂，通过显着改变多体波函数的空间结构，导致纠缠结构的深刻变化。此外，对于一类初始状态，这种变化导致腔内各处都接近热平衡，其中量子混沌中众所周知的埃伦菲斯特时间作为热化时间。具体来说，不同空间尺度下各种相关函数的量子期望值均由费米-狄拉克分布决定。此外，通过使用约化密度矩阵（RDM）和纠缠熵（EE）作为局部探针，我们发现即使整个系统处于纯净状态，子系统内部的气体与外部处于平衡状态，其热熵为EE。作为这项工作的副产品，我们提供了一个解析解，支持关于热化的重要猜想，该猜想由 Garrison 和 Grover 在《物理学》中提出并进行了数值研究。 Rev. X 8, 021026 (2018)，并强化其声明。
The exchange interaction arising from the particle indistinguishability is of central importance to physics of many-particle quantum systems. Here we study analytically the dynamical generation of quantum entanglement induced by this interaction in an isolated system, namely, an ideal Fermi gas confined in a chaotic cavity, which evolves unitarily from a non-Gaussian pure state. We find that the breakdown of the quantum-classical correspondence of particle motion, via dramatically changing the spatial structure of many-body wavefunction, leads to profound changes of the entanglement structure. Furthermore, for a class of initial states, such change leads to the approach to thermal equilibrium everywhere in the cavity, with the well-known Ehrenfest time in quantum chaos as the thermalization time. Specifically, the quantum expectation values of various correlation functions at different spatial scales are all determined by the Fermi-Dirac distribution. In addition, by using the reduced density matrix (RDM) and the entanglement entropy (EE) as local probes, we find that the gas inside a subsystem is at equilibrium with that outside, and its thermal entropy is the EE, even though the whole system is in a pure state. As a by-product of this work, we provide an analytical solution supporting an important conjecture on thermalization, made and numerically studied by Garrison and Grover in: Phys. Rev. X 8, 021026 (2018), and strengthen its statement.