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Updated: Aug 28, 2025
09:19
Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
Published on: July 29, 2013
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Super-Universality in Anderson Localization
Ivan Horváth1,2, Peter Markoš3
1University of Kentucky, Lexington, Kentucky 40506, USA.
Physical Review Letters
|September 16, 2022
Summary
We calculated the effective spatial dimension (d_IR) for electron modes in 3D Anderson models. Results suggest a super-universal value of approximately 2.665, offering insights into Anderson transitions and localization.
Area of Science:
- Condensed matter physics
- Disordered systems
Background:
- Anderson localization describes the suppression of electron wave propagation in disordered materials.
- Understanding the critical behavior of disordered systems is crucial for various physical phenomena.
Purpose of the Study:
- To calculate the effective spatial dimension (d_IR) of electron modes at critical points.
- To investigate the universality classes of 3D Anderson models.
- To explore the implications of d_IR for Anderson transitions and localization.
Main Methods:
- Calculation of the effective spatial dimension (d_IR) using a measure-based dimension of Minkowski-Hausdorff type.
- Analysis of 3D Anderson models across different universality classes (O, U, S, AIII).
Main Results:
- The effective spatial dimension (d_IR) was found to be consistent across different universality classes.
- A super-universal value of d_IR ≈ 2.665 (8/3) was suggested.
- The results indicate a unique spatial geometry associated with Anderson transitions.
Conclusions:
- The super-universal value of d_IR provides a potential marker for natural processes driven by Anderson localization.
- This finding offers new insights into the spatial geometry of Anderson transitions.
- The effective spatial dimension is a valuable tool for characterizing probability-induced subsets in disordered systems.
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