Mean quantum percolation

Mean field frozen percolation

We define a modification of the Erdős-Rényi random graph process which can be regarded as the mean field frozen percolation process. We describe the behavior of the process using differential equations and investigate their solutions in order to show the self-organized critical and extremum properties of the critical frozen percolation model. We prove two limit theorems about the distribution o...

Localization and Quantum Percolation

Electronic wave functions are studied on dilute lattices, at dimensionalities 1⩽d⩽8. Generalized average inverse participation ratios are expanded in powers of the bond concentration, p. Dlog Padé approximants indicate that these ratios diverge as (pq−p)-γq, signaling the appearance of extended states for p>pq. These Anderson transitions occur above classical percolation. No divergence is detec...

Quantum Percolation in Disordered Structures

Localization in 2D quantum percolation

Quantum site percolation as a limiting case of binary alloy is studied numerically in 2D within the tightbinding model. We address the transport properties in all regimes ballistic, diffusive (metallic), localized and crossover between the latter two. Special attention is given to the region close to the conduction band center, but even there the Anderson localization persists, without signs of...

Quantum percolation in magnetic fields.

A generalized average inverse participation ratio, for the one-electron wave functions of a dilute tight-binding model on a d-dimensional hypercubic lattice, is studied at finite magnetic fields. Extended wave functions appear above a quantum threshold bond concentration, pq. This threshold decreases at small magnetic fields, and shows a periodic dependence on the magnetic flux through a basic ...