Anderson Transition for Classical Transport in Composite Materials.

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.