Scarring in classical chaotic dynamics with noise

TL;DR

This paper demonstrates the phenomenon of classical scarring in noisy chaotic systems, showing probability density enhancement around unstable periodic orbits in classical operators, with explanations based on Lyapunov exponents and noise effects.

Contribution

It provides the first numerical evidence of classical scarring in noisy chaotic maps and draws parallels with quantum scars, offering mechanistic insights into phase-space localization.

Findings

Classical scarring observed in noisy Anosov and Bunimovich systems.

Localization explained via finite-time Lyapunov exponents.

Classical scars measurable through autocorrelation functions.

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.