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Fredholm methods for billiard eigenfunctions in the coherent state representation

Simonotti1, Saraceno

  • 1Departamento de Fisica, Comision Nacional de Energia Atomica, Avenida Libertador 8250, (1429) Buenos Aires, Argentina.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
Summary

Researchers developed a semiclassical method to represent stadium eigenfunctions using quantum mechanics and classical physics. This approach links quantum properties to classical invariants like periodic orbits.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Mathematical physics

Background:

  • Understanding quantum eigenfunctions in complex systems like stadiums is challenging.
  • Semiclassical methods bridge quantum and classical descriptions.

Purpose of the Study:

  • To derive a semiclassical expression for the projector onto eigenfunctions.
  • To obtain a semiclassical Husimi representation of stadium eigenfunctions.

Main Methods:

  • Utilizing Fredholm theory to derive the projector.
  • Expressing the projector in the coherent state basis.

Main Results:

  • A semiclassical expression for the projector onto eigenfunctions was obtained.
  • The semiclassical Husimi representation of stadium eigenfunctions was derived.

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Conclusions:

  • The Husimi representation is expressed using classical invariants: periodic points, monodromy matrices, and Maslov indices.
  • This work provides a new perspective on the semiclassical nature of stadium eigenfunctions.