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Probabilistic description of dissipative chaotic scattering.
Lachlan G Burton1, Holger R Dullin1, Eduardo G Altmann1
1School of Mathematics and Statistics, The University of Sydney, Sydney, New South Wales 2006, Australia.
Physical Review. E
|December 20, 2023
Summary
Dissipation in chaotic scattering systems can be understood from conservative systems. The survival probability in dissipative systems relates to the escape rate and conditionally invariant measure of conservative systems.
Area of Science:
- * Physics
- * Nonlinear Dynamics
- * Statistical Mechanics
Background:
- * Chaotic scattering systems exhibit complex dynamics.
- * Dissipation introduces unique finite-time behaviors in survival probability.
- * Understanding these behaviors is crucial for predicting system evolution.
Purpose of the Study:
- * To determine how probabilistic properties of dissipative chaotic scattering systems relate to their conservative counterparts.
- * To analyze the influence of dissipation on survival probability decay.
- * To connect finite-time regimes in dissipative systems to conservative system properties.
Main Methods:
- * Theoretical analysis of chaotic scattering systems with dissipation.
- * Calculation of effective escape rates, including nonhyperbolic regimes.
- * Application of conditionally invariant measure concepts.
- * Numerical simulations using the Hénon-Heiles model.
Main Results:
- * Exponential decay of survival probability (P(t)∼e^{-κt}) observed in fully chaotic systems, with escape rate (κ) energy-dependent.
- * Dissipation introduces distinct finite-time regimes in survival probability.
- * These regimes are explained by the conservative system's escape rate until a critical energy.
- * Surviving trajectories in dissipative systems follow the conservative system's conditionally invariant measure at corresponding energies.
Conclusions:
- * The probabilistic properties of dissipative chaotic scattering systems can be effectively understood from their conservative counterparts.
- * The escape rate and conditionally invariant measure of conservative systems provide key insights into dissipative system dynamics.
- * The Hénon-Heiles model validates the theoretical predictions for small dissipation and long times.
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