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Related Experiment Videos

Topology dependent quantities at the anderson transition

Slevin1, Ohtsuki, Kawarabayashi

  • 1Department of Physics, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan.

Physical Review Letters
|October 6, 2000
PubMed
Summary

Boundary conditions significantly affect scaling functions and conductance distributions in 3D Anderson transitions. However, critical disorder and exponents remain unaffected by these boundary conditions.

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Area of Science:

  • Condensed matter physics
  • Disordered systems
  • Quantum transport

Background:

  • The Anderson transition describes the metal-insulator transition in disordered electronic systems.
  • Understanding critical phenomena in such systems is crucial for condensed matter physics.
  • Boundary conditions can influence system behavior, particularly near critical points.

Purpose of the Study:

  • To investigate the impact of boundary conditions on the critical behavior of the three-dimensional Anderson transition.
  • To determine which aspects of critical behavior are sensitive to boundary conditions and which are not.

Main Methods:

  • Numerical simulations of the Anderson transition model in three dimensions.
  • Analysis of scaling functions and critical conductance distributions.

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  • Varying boundary conditions (e.g., periodic, anti-periodic, open) to assess their effects.

    • Main Results:

    • A strong dependence of the scaling function on boundary conditions was observed.
    • The critical conductance distribution was found to be significantly influenced by boundary conditions.
    • The critical disorder and critical exponent were determined to be independent of the boundary conditions studied.

    Conclusions:

    • Boundary conditions play a crucial role in shaping the detailed characteristics of the Anderson transition, such as scaling functions and conductance distributions.
    • Fundamental critical parameters like the critical disorder and critical exponent are robust and do not depend on the chosen boundary conditions for the 3D Anderson transition.