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arXiv · 2101.08362

Scarring in classical chaotic dynamics with noise

Domenico Lippolis·Akira Shudo·Kensuke Yoshida·Hajime Yoshino
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Abstract

We report the numerical observation of scarring, that is enhancement of probability density around unstable periodic orbits of a chaotic system, in the eigenfunctions of the classical Perron-Frobenius operator of noisy Anosov ("cat") maps, as well as in the noisy Bunimovich stadium. A parallel is drawn between classical and quantum scars, based on the unitarity or non-unitarity of the respective propagators. For uniformly hyperbolic systems such as the cat map, we provide a mechanistic explanation for the classical phase-space localization detected, based on the distribution of finite-time Lyapunov exponents, and the interplay of noise with deterministic dynamics. Classical scarring can be measured by studying autocorrelation functions and their power spectra.

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Domenico Lippolis, Akira Shudo, Kensuke Yoshida, Hajime Yoshino. 2021-01-20. Scarring in classical chaotic dynamics with noise. https://doi.org/10.1103/physreve.103.l050202

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