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Multifractal analysis with the probability density function at the three-dimensional anderson transition.

Alberto Rodriguez1, Louella J Vasquez, Rudolf A Römer

  • 1Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom. A.Rodriguez-Gonzalez@warwick.ac.uk

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Summary
This summary is machine-generated.

This study analyzes the probability density function (PDF) of critical wave function amplitudes in the Anderson model. The PDF reveals non-Gaussian behavior and provides insights into multifractal properties at criticality.

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Area of Science:

  • Condensed matter physics
  • Disordered systems
  • Quantum mechanics

Background:

  • The Anderson model describes electron localization in disordered materials.
  • Multifractal analysis is crucial for characterizing complex systems at criticality.

Purpose of the Study:

  • To investigate the probability density function (PDF) of critical wave function amplitudes in the 3D Anderson model.
  • To establish a connection between the PDF and the multifractal spectrum f(alpha).

Main Methods:

  • Formal expression relating PDF and multifractal spectrum f(alpha).
  • Analysis of finite-size corrections.
  • Extraction of multifractal information from the PDF.

Main Results:

  • Demonstration of non-Gaussian nature and symmetry in the PDF.
  • Identification of negative fractal dimensions and potential termination points from the PDF.
  • Validation of PDF-based multifractal analysis as an alternative method.

Conclusions:

  • The PDF of critical wave function amplitudes contains rich multifractal information.
  • PDF-based analysis offers a viable alternative to traditional methods for studying disordered systems.