Krylov空间中的经典混沌特征
Classical chaotic signatures in Krylov space
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中文总结 AI 辅助
本研究揭示经典混沌的拉伸与混合特征在Krylov空间中分别由Lyapunov指数和Ruelle-Pollicott共振体现，为量子映射的混沌研究提供新框架。
中文摘要 AI 辅助
近年来，Krylov空间方法已成为表征各种物理系统中动态混沌的有用框架。然而，Krylov动力学与经典混沌既有结构之间的联系在很大程度上仍未得到探索。经典混沌的特征是指数拉伸和混合。对于具有经典极限的量子映射，我们证明这两个特征编码在Krylov空间内的不同结构中：拉伸编码在由Lyapunov指数决定的Krylov算子的几何中，而混合则表现为Arnoldi序列的指数衰减，这与Ruelle-Pollicott共振一致。
英文摘要
In recent years, Krylov space approaches have emerged as a useful framework for characterizing dynamical chaos in a wide variety of physical systems. However, the connection between Krylov dynamics and the established structures of classical chaos remains largely unexplored. Classical chaos is characterized by exponential stretching and mixing. For quantum maps with a classical limit, we show that these two signatures are encoded in different structures within Krylov space: stretching is encoded in the geometry of the Krylov operators as determined by the Lyapunov exponent, while mixing manifests itself as an exponential decay of the Arnoldi sequences in agreement with the Ruelle-Pollicott resonances.
发表机构
- Universidad de Buenos Aires（布宜诺斯艾利斯大学）
- CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA)（阿根廷国家科学研究委员会-布宜诺斯艾利斯大学，布宜诺斯艾利斯物理研究所）
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