2000/12/07 by Arul Lakshminarayan · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaos-based Image/Signal Encryption #Chaotic #Eigenfunction #Eigenvalues and eigenvectors #Linear subspace #Mathematics #Physics #Pure mathematics #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum decoherence #Quantum dynamics #Quantum entanglement #Quantum mechanics #Von Neumann entropy #Wave function #nlin.CD #quant-ph
paper · pdf · doi:10.1103/physreve.64.036207
21 pages including 9 figs. (revtex)
arxiv created 2000/12/07 · openalex publication_date 2001/08/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.