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Semiclassical spatial correlations in chaotic wave functions.

Fabricio Toscano1, Caio H Lewenkopf

  • 1Instituto de Física, Universidade do Estado do Rio de Janeiro, R. São Francisco Xavier 524, 20559-900 Rio de Janeiro, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 23, 2002
PubMed
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We analyzed the spatial autocorrelation of energy eigenfunctions in chaotic systems. Our findings reveal how spectral averaging and spatial separation influence this autocorrelation, providing new expressions for its calculation.

Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Chaos theory

Background:

  • Studying spatial autocorrelation of energy eigenfunctions is crucial for understanding quantum chaotic systems.
  • The Weyl-Wigner formalism provides a framework for analyzing quantum systems in the semiclassical regime.

Purpose of the Study:

  • To investigate the spatial autocorrelation of energy eigenfunctions in classically chaotic systems.
  • To analyze the interplay between spectral averaging and spatial separation scales.
  • To derive new expressions for spatial autocorrelation valid for any separation size.

Main Methods:

  • Utilizing the Weyl-Wigner formalism.
  • Calculating the spectral average of the product of energy eigenfunctions (C(epsilon)(q(+),q(-),E)).

Related Experiment Videos

  • Analyzing the Fourier transform of the spectral Wigner function.

    • Main Results:

    • Revealed the chord structure of C(epsilon) inherited from the spectral Wigner function.
    • Demonstrated the interplay between the spectral average window size and spatial separation scale.
    • Derived a bridging expression and new formulas for C(epsilon) applicable to all separation sizes.

    Conclusions:

    • The spatial autocorrelation of energy eigenfunctions in chaotic systems exhibits a chord structure dependent on spectral averaging and spatial separation.
    • New expressions are derived that generalize previous formulas and are valid for any spatial separation.
    • Conditions for a local, system-independent regime of spatial autocorrelation are discussed.