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Scarring in classical chaotic dynamics with noise
Domenico Lippolis1, Akira Shudo2, Kensuke Yoshida2
1Institute for Applied Systems Analysis, Jiangsu University, Zhenjiang 212013, China.
Physical Review. E
|June 17, 2021
Summary
Researchers observed classical scarring, an enhancement of probability density near unstable periodic orbits in chaotic systems. This phenomenon was found in noisy dynamical systems, drawing parallels with quantum scarring.
Area of Science:
- * Physics
- * Dynamical Systems Theory
- * Chaos Theory
Background:
- * Scarring, the enhancement of probability density around unstable periodic orbits, is a known phenomenon in quantum mechanics.
- * Classical systems exhibiting chaotic dynamics also display similar behaviors, though less understood.
- * The role of noise in classical scarring and its relation to quantum scarring requires further investigation.
Purpose of the Study:
- * To numerically observe and characterize classical scarring in the eigenfunctions of the classical Perron-Frobenius operator.
- * To investigate the presence of scarring in specific chaotic systems: noisy Anosov maps and the noisy Bunimovich stadium.
- * To establish parallels between classical and quantum scarring and provide a mechanistic explanation for classical scarring.
Main Methods:
- * Numerical simulations of noisy Anosov maps (perturbed cat maps) and the noisy Bunimovich stadium.
- * Analysis of eigenfunctions of the classical Perron-Frobenius operator.
- * Examination of finite-time Lyapunov exponents and autocorrelation functions to explain phase-space localization.
Main Results:
- * Numerical observation of classical scarring in the eigenfunctions of the classical Perron-Frobenius operator for the studied systems.
- * Demonstration of a parallel between classical and quantum scars, linked to propagator unitarity/nonunitarity.
- * Mechanistic explanation for classical scarring in uniformly hyperbolic systems, involving finite-time Lyapunov exponents and noise-deterministic dynamics interplay.
Conclusions:
- * Classical scarring is observable in noisy chaotic systems, specifically in the eigenfunctions of the Perron-Frobenius operator.
- * The study provides a framework for understanding classical scarring and its connection to quantum scarring.
- * Autocorrelation functions and their power spectra are identified as measurable indicators of classical scarring.
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