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Related Experiment Videos

Response function of an irregular oscillator.

H Aiba1, T Suzuki

  • 1Koka Women's College, 38 Kadono-cho Nishikyogoku, Ukyo-ku, 615-0882 Kyoto, Japan.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
Summary

This study explores response functions in a two-dimensional quartic oscillator, revealing a persistent structure even in chaotic systems. This finding offers insights into quantum chaos and spectral properties.

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Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Chaos theory

Background:

  • The behavior of quantum systems, particularly their spectral and eigenstate properties, can transition between regular and chaotic regimes.
  • Response functions are crucial for understanding how quantum systems react to external influences.

Purpose of the Study:

  • To investigate the properties of response functions for a two-dimensional quartic oscillator.
  • To analyze how coupling parameters influence the regular or chaotic nature of the system's spectra and eigenstates.
  • To examine the fluctuation properties of energy-strength correlations within the response functions.

Main Methods:

  • Diagonalization of the Hamiltonian in a large model space.
  • Analysis of response functions for specific momentum transfers.
  • Investigation of energy-strength correlations.

Main Results:

  • Response functions exhibit a typical structure, even when the system's statistical properties suggest a chaotic character.
  • This structure in the response function persists and resembles that found in regular systems.
  • The coupling parameter significantly influences the transition between regular and chaotic dynamics.

Conclusions:

  • A characteristic structure exists in the response function of a two-dimensional quartic oscillator, irrespective of the system's overall regularity or chaos.
  • This persistent structure provides a deeper understanding of quantum chaos and its manifestations in spectral properties.

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