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Related Experiment Videos

Nodal domain statistics for quantum maps, percolation, and stochastic Loewner evolution.

J P Keating1, J Marklof, I G Williams

  • 1School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom.

Physical Review Letters
|August 16, 2006
PubMed
Summary

We developed a percolation model for quantum chaotic wave functions. This model accurately predicts nodal domain statistics and suggests conformal invariance in the semiclassical limit.

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Area of Science:

  • Quantum Chaos
  • Statistical Physics

Background:

  • Quantum chaotic systems exhibit complex wave function structures.
  • Nodal domains, regions where wave functions are zero, are key to understanding this complexity.

Purpose of the Study:

  • To develop a percolation model for nodal domains in quantum chaotic systems.
  • To investigate the statistical properties and boundary behavior of these nodal domains.

Main Methods:

  • Developed a percolation model based on random matrix theory.
  • Applied the model to perturbed cat maps.
  • Analyzed nodal domain statistics and boundary properties.

Main Results:

  • The percolation model accurately predicts statistical properties of nodal domains.

Related Experiment Videos

  • Nodal domains of perturbed cat maps follow the Cardy crossing formula.
  • Evidence suggests boundaries are described by stochastic Loewner evolution.

    • Conclusions:

    • Percolation theory is a valid approach for describing wave functions in Hamiltonian systems.
    • Quantum chaotic wave functions may exhibit conformal invariance in the semiclassical limit.