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Correlation function bootstrapping in quantum chaotic systems.

L Kaplan1

  • 1Department of Physics, Tulane University, New Orleans, Louisiana 70118, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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This study introduces a method to predict long-term quantum system behavior from short-time data. It works for individual systems or ensembles, offering stable approximations for dynamics and properties.

Area of Science:

  • Quantum mechanics
  • Computational physics

Background:

  • Chaotic and complex quantum systems exhibit intricate dynamics.
  • Understanding long-time dynamics and stationary properties is crucial in quantum physics.

Purpose of the Study:

  • To develop an efficient approach for "bootstrapping" short-time correlation data.
  • To extract long-time dynamics and stationary properties from limited data.
  • To provide a method applicable to both individual quantum systems and ensembles.

Main Methods:

  • Utilizing short-time correlation data as input.
  • Applying a bootstrapping technique to infer long-time behavior.
  • Developing systematic approximations for spectra and wave functions.
  • Analyzing statistical properties for ensembles of quantum systems.

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Main Results:

  • A general and efficient method for predicting long-time quantum dynamics.
  • Accurate approximations for spectrum and wave functions when individual systems are identifiable.
  • Reliable statistical properties, including wave function intensity distributions, for ensembles.
  • Robustness of the method against perturbations in short-time input data.

Conclusions:

  • The bootstrapping approach effectively bridges short-time data to long-time quantum system properties.
  • The method is versatile, applicable to open/closed systems and various quantum models.
  • This technique offers a powerful tool for analyzing complex quantum dynamics.