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Related Experiment Videos

Classical intermittency and the quantum Anderson transition.

Antonio M García-García1

  • 1Laboratoire de Physique Théorique et Modèles Statistiques, Bâtiment 100, Université de Paris-Sud, 91405 Orsay Cedex, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 13, 2004
PubMed
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Quantum systems with intermittent classical counterparts exhibit spectral correlations linked to anomalous diffusion operators. These properties resemble disordered systems at the Anderson transition, offering insights into quantum chaos.

Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Chaos theory

Background:

  • Intermittency in classical systems leads to complex dynamics.
  • Quantum spectral correlations are key to understanding quantum chaos.
  • Semiclassical methods bridge classical and quantum descriptions.

Purpose of the Study:

  • To investigate quantum systems with classical intermittency.
  • To connect quantum spectral correlations to anomalous diffusion.
  • To explore implications for disordered systems and quantum Hamiltonians.

Main Methods:

  • Application of recent semiclassical techniques.
  • Analysis of quantum spectral correlations.
  • Eigenvalue analysis of an anomalous diffusion operator.

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Main Results:

  • Quantum spectral correlations are determined by anomalous diffusion operator eigenvalues.
  • Similarities observed between spectral properties and Anderson transition in disordered systems.
  • Connection established between classical intermittency, cantori, and quantum spectral correlations.

Conclusions:

  • Findings offer a new perspective on quantum spectral correlations in systems with classical intermittency.
  • The study suggests relevance for Hamiltonians with phase spaces filled with cantori.
  • Results extend to higher dimensions and relate to Anderson models with long-range hopping.