Classical chaotic signatures in Krylov space

Abstract

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.