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Updated: Aug 9, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Relaxation to the invariant density for the kicked rotor
Summary
This study analytically calculates relaxation rates for the kicked rotor model, revealing diffusion modes in momentum and intermixed dynamics in angle and momentum spaces. These findings offer insights into chaotic systems dynamics.
Area of Science:
- * Physics
- * Statistical Mechanics
- * Dynamical Systems
Background:
- * The kicked rotor, a standard map model, exhibits chaotic behavior.
- * Understanding relaxation rates to invariant density is crucial for chaotic systems.
- * Analytical solutions for mixed systems like the kicked rotor are challenging.
Purpose of the Study:
- * To analytically calculate relaxation rates in the chaotic phase space of the kicked rotor.
- * To investigate the influence of noise and its vanishing limit on these rates.
- * To characterize the nature of slow and fast relaxation modes.
Main Methods:
- * Analytical calculation of relaxation rates using the resolvent operator.
- * Leading order calculations in 1/sqrt[K] for large stochasticity.
- * Analysis of diffusion modes and dynamics of inhomogeneities in angle space.
- * Verification through numerical simulations.
Main Results:
- * Leading relaxation rates were calculated analytically to the order of 1/sqrt[K].
- * Finite relaxation rates were found in the vanishing noise limit, with poles inside the unit circle.
- * Slow rates correspond to diffusion in momentum; faster rates intermix angle and momentum dynamics.
- * The slowest relaxation rate in angle space was derived by studying inhomogeneity dynamics.
Conclusions:
- * Analytical results confirm finite relaxation rates for the kicked rotor, consistent with poles inside the unit circle.
- * The study elucidates the distinct behaviors of slow (diffusion) and faster (intermixed) relaxation modes.
- * The findings provide a detailed analytical understanding of relaxation dynamics in a paradigmatic chaotic system.
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