Lakshminarayan A
Physical Research Laboratory, Navrangpura, Ahmedabad 380 009, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 2):036207. doi: 10.1103/PhysRevE.64.036207. Epub 2001 Aug 20.
We study the quantum entanglement caused by unitary operators that have classical limits that can range from the near integrable to the completely chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is studied through the von Neumann entropy of the reduced density matrices. We demonstrate that classical chaos can lead to substantially enhanced entanglement. Conversely, entanglement provides a useful characterization of quantum states in higher-dimensional chaotic or complex systems. Information about eigenfunction localization is stored in a graded manner in the Schmidt vectors, and the principal Schmidt vectors can be scarred by the projections of classical periodic orbits onto subspaces. The eigenvalues of the reduced density matrices is sensitive to the degree of wave-function localization, and is roughly exponentially arranged. We also point out the analogy with decoherence, as reduced density matrices corresponding to subsystems of fully chaotic systems, are diagonally dominant.
我们研究由具有经典极限的酉算子所引起的量子纠缠，这些经典极限范围可以从近可积到完全混沌。通过约化密度矩阵的冯·诺依曼熵来研究本征态和随时间演化的任意态中的纠缠。我们证明经典混沌可导致显著增强的纠缠。反之，纠缠为高维混沌或复杂系统中的量子态提供了一种有用的表征。关于本征函数局域化的信息以分级方式存储在施密特向量中，并且主要施密特向量会因经典周期轨道在子空间上的投影而出现疤痕。约化密度矩阵的本征值对波函数的局域化程度敏感，并且大致呈指数排列。我们还指出了与退相干的类比，因为对应于完全混沌系统子系统的约化密度矩阵是对角占优的。
