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Related Experiment Videos

Chaotic spectroscopy.

Eyal Doron1, Uzy Smilansky

  • 1Department of Nuclear Physics, The Weizmann Institute of Science, Rehovot 76100, IsraelH. H. Wills Physics Laboratory, Royal Fort, Tyndall Avenue, Bristol BS8 1TL, United Kingdom.

Chaos (Woodbury, N.Y.)
|January 1, 1992
PubMed
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Quantized chaotic billiards exhibit spectral and resonance densities that fluctuate around a common mean. This phenomenon is explained using semiclassical methods, linking classical scattering and periodic orbits for a novel interpretation of spectral density.

Area of Science:

  • Quantum mechanics
  • Scattering theory
  • Statistical physics

Background:

  • Chaotic billiards are quantum systems exhibiting complex spectral properties.
  • Understanding spectral fluctuations is key to characterizing quantum chaos.

Purpose of the Study:

  • To discuss the spectra of quantized chaotic billiards using scattering theory.
  • To explain the fluctuation of spectral and resonance densities.
  • To provide a new interpretation of Gutzwiller's periodic orbits sum.

Main Methods:

  • Scattering theory approach.
  • Semiclassical treatment.
  • Analysis of classical scattering trajectories and periodic orbits of the Poincare scattering map.

Main Results:

Related Experiment Videos

  • Spectral and resonance density functions fluctuate around a common mean.
  • A semiclassical explanation is provided linking classical dynamics to spectral properties.
  • An alternative derivation and interpretation of Gutzwiller's periodic orbits sum is presented.

Conclusions:

  • The scattering theory formalism offers a new perspective on spectral density in chaotic billiards.
  • This framework facilitates the derivation of Riemann-Siegel-like expressions for the secular equation.