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Eigenstate structure in graphs and disordered lattices.

L Kaplan1

  • 1Institute for Nuclear Theory and Department of Physics, University of Washington, Seattle, Washington 98195, USA. lkaplan@phys.washington.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 3, 2001
PubMed
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Quantum graph wave functions show less ergodicity than random matrix theory predicts, despite matching spectral statistics. Short-time semiclassical analysis accurately describes the eigenstate structure in chaotic and disordered systems.

Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Mathematical physics

Background:

  • Quantum graphs are models for complex systems.
  • Chaotic and disordered regimes present unique quantum phenomena.
  • Random matrix theory (RMT) is often used to predict spectral statistics.

Purpose of the Study:

  • Investigate wave function structure in quantum graphs.
  • Compare ergodicity measures with RMT predictions.
  • Identify suitable methods for describing eigenstate structure.

Main Methods:

  • Analysis of wave function intensity distribution.
  • Calculation of the inverse participation ratio.
  • Application of short-time semiclassical approximations.

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Main Results:

  • Observed significantly less ergodicity than predicted by RMT.
  • Confirmed spectral statistics align with RMT predictions.
  • Demonstrated the efficacy of semiclassical methods for eigenstate structure.

Conclusions:

  • Standard RMT may not fully capture wave function properties in quantum graphs.
  • Semiclassical methods offer a more accurate description of eigenstate localization.
  • Understanding wave function structure is crucial for chaotic and disordered quantum systems.