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Quantum transport through cantori

Maitra1, Heller

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138 and Harvard-Smithsonian Center for Astrophysics, Harvard University, Cambridge, Massachusetts 02138, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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Classical cantori create quantum transport barriers, even when Planck's constant is small. A new "retunneling" mechanism emerges as Planck's constant increases, impacting quantum localization.

Area of Science:

  • Quantum mechanics
  • Classical dynamics
  • Chaos theory

Background:

  • Classical cantori are known to influence quantum transport.
  • Previous studies focused on specific regimes of Planck's constant relative to cantorus flux.

Purpose of the Study:

  • To investigate the role of classical cantori in quantum mechanics across different regimes of Planck's constant.
  • To elucidate the mechanisms of quantum localization induced by cantori.
  • To provide a phase space perspective on cantori in quantum mechanics.

Main Methods:

  • Analysis of quantum transport in the presence of cantori.
  • Investigation of Planck's constant dependence on localization mechanisms.
  • Development of a phase space visualization for cantori.

Related Experiment Videos

  • Utilizing the whisker map for illustration.

    • Main Results:

    • Cantori form exponential barriers to quantum transport regardless of whether Planck's constant is larger or smaller than the cantorus flux.
    • A transition from dynamical localization to "retunneling" occurs as Planck's constant increases.
    • The Planck's constant dependence of exponential decay for retunneling is consistent with previous findings, even away from criticality.

    Conclusions:

    • Classical cantori play a crucial role in quantum transport barriers across various physical regimes.
    • The newly identified "retunneling" mechanism offers a deeper understanding of quantum localization.
    • The study provides a comprehensive phase space view of cantori in quantum mechanics.