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arXiv · 2112.11694

Stochastic modeling of spreading and dissipation in mixed-chaotic systems that are driven quasistatically

Yehoshua Winsten·Doron Cohen
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Abstract

We analyze energy spreading for a system that features mixed chaotic phase-space, whose control parameters (or slow degrees of freedom) vary quasi-statically. For demonstration purpose we consider the restricted 3~body problem, where the distance between the two central stars is modulated due to their Kepler motion. If the system featured hard-chaos, one would expect diffusive spreading with coefficient that can be estimated using linear-response (Kubo) theory. But for mixed phase space the chaotic sea is multi-layered. Consequently, it becomes a challenge to find a robust procedure that translates the sticky dynamics into a stochastic model. We propose a Poincar\'e-sequencing method that reduces the multi-dimensional motion into a one-dimensional random-walk in impact-space. We test the implied relation between stickiness and the rate of spreading.

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Yehoshua Winsten, Doron Cohen. 2021-12-22. Stochastic modeling of spreading and dissipation in mixed-chaotic systems that are driven quasistatically. https://doi.org/10.1103/physreve.105.054113

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