Universal Exponent for Transport in Mixed Hamiltonian Dynamics

Abstract

We compute universal distributions for the transition probabilities of a Markov model for transport in the mixed phase space of area-preserving maps and verify that the survival probability distribution for trajectories near an infinite island-around-island hierarchy exhibits, on average, a power law decay with exponent $\gamma =1.57$. This exponent agrees with that found from simulations of the Hénon and Chirikov-Taylor maps. This provides evidence that the Meiss-Ott Markov tree model describes the transport for mixed systems.

arXiv comment8 pages

References in corpus (8)

• Long-Time Correlations in the Stochastic Regime
• On universality of algebraic decays in Hamiltonian systems
• Average exit times in volume preserving maps
• Effect of Noise on the Standard Mapping
• Generic Twistless Bifurcations
• Statistics of the Island-Around-Island Hierarchy in Hamiltonian Phase Space
• Fluctuations in the relaxation dynamics of mixed chaotic systems
• Poincaré recurrences and Ulam method for the Chirikov standard map

Cited by in corpus (12)

• Rotational random walk of the harmonic three body system
• 3D billiards: visualization of regular structures and trapping of chaotic trajectories
• Accelerator modes and anomalous diffusion in 3D volume-preserving maps
• Regular Regimes of the Three Body Harmonic System
• Conservative, Dissipative and Super-diffusive Behavior of a Particle Propelled in a Regular Flow
• Small world of Ulam networks for chaotic Hamiltonian dynamics
• Phase-space study of surface-electrode Paul traps: Integrable, chaotic, and mixed motions
• Diffusion Phenomena in a Mixed Phase Space
• Power-law trapping in the volume-preserving Arnold-Beltrami-Childress map
• Can a periodically driven particle resist laser cooling and noise?
• Recurrence and Stickiness in the Noisy Harper Map
• Quantum correlations for a simple kicked system with mixed phase space