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Area of Science:

  • Physics
  • Materials Science
  • Network Theory

Background:

  • The Anderson transition describes wave function localization due to disorder in solids and optics.
  • This phenomenon is typically associated with wave interference and scattering effects.

Purpose of the Study:

  • To investigate if classical transport phenomena exhibit hallmarks of the Anderson transition.
  • To explore the role of disorder and connectedness in classical transport dynamics.

Main Methods:

  • Analysis of transport in resistor networks, human bone, and sea ice structures.
  • Examination of eigenvalue statistics of random matrices governing transport.
  • Study of field eigenvector delocalization.

Main Results:

  • Classical transport at a percolation threshold mirrors Anderson transition characteristics.
  • The transition occurs without wave interference or scattering.
  • Eigenvalue statistics crossover to universal Gaussian orthogonal ensemble statistics as order increases.
  • Field eigenvectors delocalize as long-range order develops.

Conclusions:

  • The Anderson transition concept extends beyond wave phenomena to classical transport.
  • Percolation theory provides a framework for understanding this classical Anderson transition.
  • Disordered classical systems can exhibit delocalization transitions analogous to quantum systems.