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Relaxation and diffusion for the kicked rotor

Khodas1, Fishman

  • 1Physics Department, Technion, Haifa 32000, Israel.

Physical Review Letters
|October 6, 2000
PubMed
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We statistically studied the kicked rotor, a mixed dynamical system. We found its chaotic component relaxes to equilibrium when bounded and exhibits diffusive behavior when unbounded, with results verified numerically.

Area of Science:

  • Statistical mechanics
  • Nonlinear dynamics
  • Chaos theory

Background:

  • The kicked rotor is a classic model for mixed dynamical systems, exhibiting both regular and chaotic motion.
  • Understanding the statistical properties of such systems is crucial for various fields, including physics and engineering.

Purpose of the Study:

  • To statistically analyze the dynamics of the kicked rotor, focusing on its chaotic component.
  • To investigate the relaxation rates to equilibrium density in the presence of noise and its vanishing limit.

Main Methods:

  • Calculation of the phase space density evolution operator in the chaotic component with added noise.
  • Analytical calculation of relaxation rates using an approximation that improves with increasing stochasticity.
  • Numerical verification of the analytical results.

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Main Results:

  • The study presents a global picture of relaxation dynamics in the chaotic component of the kicked rotor.
  • For bounded systems, relaxation to equilibrium density is observed.
  • For unbounded systems, diffusive behavior is identified.

Conclusions:

  • The statistical analysis provides insights into the long-term behavior of mixed systems like the kicked rotor.
  • The findings highlight the distinct relaxation pathways in bounded versus unbounded configurations.
  • The developed approximation offers a reliable method for studying systems with increasing stochasticity.