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Quantization of a billiard model for interacting particles

Papenbrock1, Prosen

  • 1Centro Internacional de Ciencias A.C., 62131 Cuernavaca, Mexico.

Physical Review Letters
|October 4, 2000
PubMed
Summary

We studied a chaotic three-body system. A new type of quantum scarring, linked to specific orbits, explains deviations from random matrix theory predictions in spectral fluctuations.

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Wave function structure in two-body random matrix ensembles

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Area of Science:

  • Quantum mechanics
  • Classical mechanics
  • Chaos theory

Background:

  • Investigating few-body systems is crucial for understanding complex interactions.
  • Billiard models offer simplified yet insightful frameworks for studying dynamical systems.
  • Chaotic dynamics in classical systems can lead to unique quantum phenomena.

Purpose of the Study:

  • To analyze the classical and quantum dynamics of a self-bound, interacting three-body system.
  • To investigate spectral fluctuations in the quantum regime and compare them with theoretical predictions.
  • To identify the underlying mechanisms causing deviations from standard random matrix theory.

Main Methods:

  • Developing and utilizing a two-dimensional billiard model for a three-body system.
  • Performing numerical simulations to study classical chaotic dynamics.
  • Analyzing quantum spectral fluctuations and their relationship to classical orbits.

Main Results:

  • The classical dynamics of the three-body system were found to be chaotic.
  • Quantum spectral fluctuations showed minor deviations from random matrix theory predictions.
  • A novel form of quantum scarring was identified, associated with collinear orbits.

Conclusions:

  • The observed deviations in spectral fluctuations are attributed to a specific type of quantum scarring.
  • This scarring phenomenon arises from a family of orbits within the collinear manifold.
  • The study provides new insights into the interplay between classical chaos and quantum behavior in few-body systems.

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