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Semiclassical quantization by harmonic inversion: comparison of algorithms.

T Bartsch1, J Main, G Wunner

  • 1Institut für Theoretische Physik 1, Universität Stuttgart, D-70550 Stuttgart, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
PubMed
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Harmonic inversion methods aid in analyzing quantum spectra for dynamical systems. This study compares computational techniques to determine the most numerically efficient approach for quantum analysis.

Area of Science:

  • Quantum mechanics
  • Classical and quantum dynamics
  • Computational physics

Background:

  • Harmonic inversion is a key technique for semiclassical quantization.
  • It is used for analyzing quantum spectra in dynamical systems, including chaotic ones.
  • Several computational methods exist for harmonic inversion.

Purpose of the Study:

  • To identify the most numerically efficient harmonic inversion method.
  • To compare the accuracy of different computational procedures.
  • To provide a guide for selecting appropriate techniques.

Main Methods:

  • Summarizing and discussing various harmonic inversion techniques.
  • Comparing the numerical efficiency and accuracy of these methods.
  • Applying the techniques to two example dynamical systems (integrable and chaotic).

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Main Results:

  • The study evaluates the performance of different harmonic inversion algorithms.
  • Accuracy and computational cost are key metrics for comparison.
  • Results highlight the strengths and weaknesses of each method for specific applications.

Conclusions:

  • The findings will guide researchers in choosing the most efficient harmonic inversion technique.
  • This comparison aids in the accurate semiclassical quantization and spectral analysis of dynamical systems.
  • The study contributes to the practical application of harmonic inversion in quantum mechanics.