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A theory of quantum diffusion localization.

Boris V. Chirikov1

  • 1Institute of Nuclear Physics, 630090 Novosibirsk, USSR.

Chaos (Woodbury, N.Y.)
|July 1, 1991
PubMed
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Quantum localization transforms chaotic motion into a steady state. This study reviews the kicked rotator model and introduces a new theory for quantum dynamical relaxation.

Area of Science:

  • Quantum dynamics
  • Statistical mechanics
  • Classical chaos

Background:

  • Chaotic diffusion in classical systems can exhibit quantum localization.
  • The kicked rotator model serves as a paradigm for studying quantum effects on classical chaos.

Purpose of the Study:

  • To review the quantum localization phenomenon in classical chaotic motion.
  • To describe the quantum steady state resulting from statistical relaxation.
  • To present and compare a new phenomenological theory of quantum dynamical relaxation.

Main Methods:

  • Review of the kicked rotator model.
  • Analysis of statistical relaxation in a discrete quantum spectrum.
  • Development and comparison of phenomenological theories for quantum dynamical relaxation.

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Main Results:

  • Detailed description of the quantum steady state achieved through statistical relaxation.
  • Presentation of a novel phenomenological theory for quantum dynamical relaxation.
  • Comparison of the new theory with existing theoretical frameworks.

Conclusions:

  • Quantum localization is a key feature of quantum systems initially exhibiting chaotic classical motion.
  • Statistical relaxation leads to a unique quantum steady state.
  • The new phenomenological theory offers a refined understanding of quantum dynamical relaxation processes.