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

TL;DR

This paper develops a stochastic model for energy spreading in mixed-chaotic systems with quasi-static parameter variation, using a Poincaré-sequencing method to handle sticky dynamics in phase space.

Contribution

It introduces a novel Poincaré-sequencing approach to model multi-layered chaotic phase-space as a one-dimensional random walk, addressing the challenge of sticky dynamics.

Findings

The model captures the relation between stickiness and spreading rate.

The approach effectively reduces multi-dimensional chaos to a one-dimensional stochastic process.

Validation shows the method's potential for complex mixed-chaotic systems.

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.