Scarring in classical chaotic dynamics with noise
arXiv:2101.08362 · doi:10.1103/PhysRevE.103.L050202
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.
arXiv comment6 pages, 6 figures
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Cited by in corpus (6)
- Eigenfunctions of the Perron-Frobenius operator and the finite-time Lyapunov exponents in uniformly hyperbolic area-preserving maps
- Thermodynamics of chaotic relaxation processes
- Chaotic fields out of equilibrium are observable independent
- Escape-rate response to noise of all amplitudes in leaky chaos
- Oscillatory and dissipative dynamics of complex probability in non-equilibrium stochastic processes
- Estimating the spectral density of unstable scars