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The periodically kicked quantum spin.

R. H. Parmenter1, L. Y. Yu

  • 1Department of Physics, University of Arizona, Tucson, Arizona 85721.

Chaos (Woodbury, N.Y.)
|October 1, 1992
PubMed
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Deterministic chaos, observed in classical systems, can also occur in quantum mechanical systems. The periodically kicked quantum spin (PKQS) model demonstrates this phenomenon, showing chaotic behavior and Arnold diffusion.

Area of Science:

  • Quantum mechanics
  • Classical mechanics
  • Chaos theory

Background:

  • Classical systems exhibit deterministic chaos.
  • Quantum systems are typically not associated with chaotic behavior.
  • Understanding quantum chaos is crucial for fundamental physics.

Purpose of the Study:

  • To investigate the occurrence of deterministic chaos in quantum mechanical many-body systems.
  • To analyze the periodically kicked quantum spin (PKQS) model as a physical realization of quantum chaos.
  • To explore the relationship between quantum and classical chaotic maps.

Main Methods:

  • Derivation of the three-dimensional PKQS map from quantum mechanical equations of motion.
  • Analysis of the PKQS map for different quantum spin values (s=1/2, s=1).

Related Experiment Videos

  • Comparison with classical chaotic systems, including Zaslavsky stochastic webs.

    • Main Results:

    • The PKQS map exhibits deterministic chaos and Arnold diffusion, analogous to classical systems.
    • The same chaotic map is observed for quantum spin s=1/2 and s=1, but not for s>=3/2.
    • Generalization of the PKQS model yields stochastic webs on a unit sphere, similar to classical stochastic webs.

    Conclusions:

    • Deterministic chaos is possible in certain quantum mechanical many-body systems.
    • The PKQS model provides a concrete example of quantum chaos with implications for both quantum and classical dynamics.
    • The study bridges the gap between quantum mechanics and classical chaos through a unified mapping approach.