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Related Experiment Videos

Localization transition on complex networks via spectral statistics.

M Sade1, T Kalisky, S Havlin

  • 1The Minerva Center, Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
PubMed
Summary
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Complex networks exhibit Anderson metal-insulator transitions, similar to disordered materials. Transition clarity depends on network connectivity, becoming less distinct in highly connected systems.

Area of Science:

  • Complex networks analysis
  • Condensed matter physics
  • Disordered systems

Background:

  • The Anderson metal-insulator transition describes the transition from a conducting to an insulating state in disordered materials.
  • Complex networks, characterized by their structure and connectivity, are increasingly studied for their physical properties.

Purpose of the Study:

  • To numerically investigate the spectral statistics of complex networks.
  • To explore the applicability of Anderson metal-insulator transition concepts to various network structures.
  • To determine how network connectivity influences the metal-insulator transition.

Main Methods:

  • Numerical simulation of spectral statistics.
  • Analysis of Anderson metal-insulator transition features across different network classes.

Related Experiment Videos

  • Systematic variation of disorder and average connectivity.

    • Main Results:

    • Similar Anderson metal-insulator transition features were observed across a wide range of complex networks.
    • A clear metal-insulator transition was identified in networks with low average connectivity as a function of disorder.
    • The critical index for these transitions matched mean-field expectations.
    • In highly connected networks, localization increased proportionally with average connectivity, but a sharp transition was not observed.
    • The lack of a distinct transition in high-connectivity networks is attributed to their compact structure and small diameter.

    Conclusions:

    • Complex networks can exhibit Anderson metal-insulator transitions, with features comparable to disordered materials.
    • Network connectivity plays a crucial role in the nature and observability of these transitions.
    • The findings suggest that network topology significantly impacts electronic localization phenomena.