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Quantum chaos in the Wigner representation.

G. P. Berman1, A. R. Kolovskii, F. M. Izrailev

  • 1L. V. Kirenskii Institute of Physics, Siberian Branch of the Academy of Sciences of the USSR, 660036 Krasnoyarsk, USSRInstitute of Nuclear Physics, Siberian Branch of the Academy of Sciences of the USSR, 630090 Novosibirsk, USSRL. V. Kirenskii Institute of Physics, Siberian Branch of the Academy of Sciences of the USSR, 660036 Krasnoyarsk, USSR.

Chaos (Woodbury, N.Y.)
|August 1, 1991
PubMed
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This study analyzes quantum kicked rotator dynamics using the Wigner representation. A simplified map accurately describes the system

Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Nonlinear dynamics

Background:

  • The quantum kicked rotator is a key model for studying stochastic behavior in quantum systems.
  • Understanding its dynamics is crucial for advancing quantum chaos research.

Purpose of the Study:

  • To analyze the dynamics of the quantum kicked rotator model.
  • To develop a simplified yet accurate representation of its behavior.

Main Methods:

  • Analysis in the Wigner representation.
  • Derivation of exact nonlocal maps on a discrete phase space.

Main Results:

  • The Wigner representation provides a framework for analyzing the quantum kicked rotator.
  • Exact nonlocal maps were successfully derived.

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  • A simplified map effectively captures the essential dynamics by considering the discrete phase space.

    • Conclusions:

    • The Wigner representation offers a powerful tool for studying quantum chaotic systems.
    • Simplified maps can satisfactorily describe complex quantum dynamics.
    • The discrete nature of phase space is a key factor in the simplified model's success.