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Semiclassical cross section correlations

Eckhardt1, Fishman, Varga

  • 1Fachbereich Physik, Philipps Universitat Marburg, D-35032 Marburg, Germany.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|January 4, 2001
PubMed
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This study introduces a semiclassical method to calculate autocorrelation functions for cross sections. It reveals two key contributions determined by classical dynamics, offering insights into quantum chaos and random matrix theory.

Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Quantum chaos

Background:

  • Understanding the behavior of quantum systems and their statistical properties is crucial.
  • Semiclassical methods bridge quantum and classical descriptions, offering computational advantages.

Purpose of the Study:

  • To develop a semiclassical approximation for calculating the autocorrelation function of cross sections.
  • To analyze the contributions to this function based on classical dynamics.
  • To connect semiclassical results with random matrix theory predictions.

Main Methods:

  • Utilizing semiclassical expressions for diagonal matrix elements of operators.
  • Analyzing the autocorrelation function of these matrix elements.
  • Applying the method to the kicked rotor model for verification.

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Main Results:

  • The autocorrelation function is shown to have two contributions.
  • The relative weights of these contributions are determined by classical dynamics.
  • The random matrix theory result is recovered when the operator approximates a projector onto a single state.

Conclusions:

  • The semiclassical approach provides a robust framework for studying autocorrelation functions.
  • Classical dynamics play a critical role in determining the statistical properties of quantum cross sections.
  • This work validates the semiclassical approximation and its connection to random matrix theory.