Relaxation and Diffusion for the Kicked Rotor

Abstract

The dynamics of the kicked-rotor, that is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular is studied statistically. The evolution (Frobenius-Perron) operator of phase space densities in the chaotic component is calculated in presence of noise, and the limit of vanishing noise is taken is taken in the end of calculation. The relaxation rates (related to the Ruelle resonances) to the invariant equilibrium density are calculated analytically within an approximation that improves with increasing stochasticity. The results are tested numerically. The global picture of relaxation to the equilibrium density in the chaotic component when the system is bounded and of diffusive behavior when it is unbounded is presented.

References in corpus (1)

• Anomalous transport and quantum-classical correspondence

Cited by in corpus (16)

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• Resonances of the Frobenius-Perron Operator for a Hamiltonian Map with a Mixed Phase Space
• Theory of localization and resonance phenomena in the quantum kicked rotor
• Relaxation to the Invariant Density for Kicked Rotor
• Ehrenfest time in the weak dynamical localization
• Weak dynamical localization in periodically kicked cold atomic gases
• The leading Ruelle resonances of chaotic maps
• Momentum dependent quantum Ruelle-Pollicott resonances in translationally invariant many-body systems
• Leading Pollicott-Ruelle Resonances and Transport in Area-Preserving Maps
• Leading Pollicott-Ruelle Resonances for Chaotic Area-Preserving Maps
• Classical approach to equilibrium of out-of-time ordered correlators in mixed systems
• Spectrum of the Frobenius-Perron operator for systems with stochastic perturbation
• Quantization of Classical Maps with tunable Ruelle-Pollicott Resonances
• Non-Gaussian features of chaotic Hamiltonian transport
• Diffusion For Ensembles of Standard Maps
• Ruelle-Pollicott Decay of Out-of-Time-Order Correlators in Many-Body Systems