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Related Experiment Videos

Correlations in quantum time delay.

Bruno Eckhardt1

  • 1Fachbereich Physik und Institut fur Chemie und Biologie des Meeres, Carl von Ossietzky Universitat, Postfach 25 03, D-26111 Oldenburg, Germany.

Chaos (Woodbury, N.Y.)
|October 1, 1993
PubMed
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This study analyzes quantum time delay using semiclassical periodic orbits. It identifies three distinct regimes, revealing how classical escape rates and resonance lifetimes govern quantum behavior in scattering systems.

Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Chaos theory

Background:

  • The quantum time delay is a crucial observable in scattering problems, providing insights into the dynamics of quantum systems.
  • Semiclassical methods offer a powerful framework to connect classical dynamics with quantum phenomena, particularly in complex systems.

Purpose of the Study:

  • To investigate the semiclassical periodic orbit content of the form factor K(lambda) for quantum time delay.
  • To identify and characterize different regimes governing the behavior of K(lambda) based on semiclassical approximations.
  • To establish the relationship between classical escape rates, resonance lifetimes, and the observed quantum behavior.

Main Methods:

  • Fourier transform of the autocorrelation function to obtain the form factor K(lambda).

Related Experiment Videos

  • Analysis of K(lambda) in different regimes (small, intermediate, and large lambda) using semiclassical periodic orbit theory.
  • Comparison of theoretical predictions with numerical data from a three-disk scattering system.

    • Main Results:

    • Three distinct semiclassical regimes were identified for the quantum time delay form factor.
    • For small lambda, isolated periodic orbits dominate.
    • For intermediate lambda, a regime characterized by the classical escape rate (Gamma) was observed, transitioning to a resonance lifetime-dependent regime (gamma(qm)) at large lambda.

    Conclusions:

    • The semiclassical periodic orbit theory successfully describes the quantum time delay.
    • The density of resonances plays a critical role in the transition between different semiclassical regimes.
    • The findings provide a deeper understanding of quantum chaos and resonance phenomena in scattering systems.