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Pseudointegrable Andreev billiard.

Jan Wiersig1

  • 1Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany. jwiersig@mpipks-dresden.mpg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 23, 2002
PubMed
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We found that circular Andreev billiards in a magnetic field exhibit pseudointegrable classical dynamics, similar to polygonal billiards. This reveals new insights into the proximity effect in chaotic Andreev billiards.

Area of Science:

  • Quantum chaos
  • Condensed matter physics
  • Dynamical systems theory

Background:

  • Andreev billiards are quantum systems exhibiting chaotic behavior.
  • Understanding their dynamics is crucial for solid-state physics and quantum information.
  • The influence of external magnetic fields on these systems is not fully understood.

Purpose of the Study:

  • To investigate the classical dynamics of a circular Andreev billiard in a uniform magnetic field.
  • To establish connections between circular Andreev billiards and polygonal billiards.
  • To explore the implications for the proximity effect in chaotic Andreev billiards.

Main Methods:

  • Analysis of classical dynamics in a uniform magnetic field.
  • Comparison with pseudointegrable systems like rational polygonal billiards.

Related Experiment Videos

  • Numerical investigation of the Poincaré map on invariant sets.

    • Main Results:

    • Classical dynamics of the circular Andreev billiard is demonstrated to be pseudointegrable.
    • A relationship is established with the asymmetric barrier billiard.
    • Numerical evidence suggests the Poincaré map is typically weak mixing on invariant sets.

    Conclusions:

    • The study reveals a link between circular Andreev billiards and polygonal billiards, clarifying their dynamical properties.
    • The findings shed light on the proximity effect in chaotic Andreev billiards.
    • Pseudointegrability offers a new perspective on the behavior of these quantum systems.