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Related Experiment Videos

Classical singularities and semi-Poisson statistics in disordered systems.

Antonio M García-García1

  • 1Physics Department, Princeton University, Princeton, New Jersey 08544, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
PubMed
Summary
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This study reveals that semi-Poisson statistics precisely describe the level statistics of a disordered Hamiltonian with nonanalytical dispersion. This finding is robust and distinct from critical statistics found at the Anderson transition.

Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Condensed matter physics

Background:

  • Disordered systems exhibit complex energy level statistics.
  • Semi-Poisson statistics are observed in pseudointegrable systems.
  • Anderson transition describes the localization of electrons in disordered materials.

Purpose of the Study:

  • To investigate the level statistics of a one-dimensional disordered Hamiltonian with nonanalytical dispersion.
  • To determine if semi-Poisson statistics accurately describe this system.
  • To differentiate these statistics from critical statistics at the Anderson transition.

Main Methods:

  • Analysis of a one-dimensional disordered Hamiltonian.
  • Investigation of nonanalytical dispersion relations.

Related Experiment Videos

  • Comparison with deterministic kicked rotator models.

    • Main Results:

    • The energy level statistics were exactly described by semi-Poisson statistics.
    • This result was shown to be robust and independent of microscopic Hamiltonian details.
    • A deterministic kicked rotator with a steplike potential exhibited similar spectral properties.

    Conclusions:

    • Semi-Poisson statistics characterize the investigated disordered system.
    • These statistics originate from a specific type of nonanalytical potential.
    • The study provides evidence that semi-Poisson statistics differ from critical Anderson transition statistics, each arising from distinct classical singularities.