Numerical study of quantum percolation

Numerical study of a field theory for directed percolation.

A numerical method is devised for study of stochastic partial differential equations (SPDEs) describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened sensitivity to fluctuations attending multiplicative noise in the vicinity of an absorbing state, a useful method requires discretization of the field variab...

Explosive percolation: a numerical analysis.

Percolation is one of the most studied processes in statistical physics. A recent paper by Achlioptas [Science 323, 1453 (2009)] showed that the percolation transition, which is usually continuous, becomes discontinuous ("explosive") if links are added to the system according to special cooperative rules (Achlioptas processes). In this paper, we present a detailed numerical analysis of Achliopt...

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...

A study of the two-dimensional bond quantum percolation model

The nature of the electronic states of the two-dimensional bond quantum percolation model is investigated using the finite size scaling method. The results indicate that at all concentrations above the percolation concentration the states are exponentially localised. There is no delocalisation transition. The scaling behaviour of the model is found to be the same as for the normal Anderson mode...

Quantum Percolation in Disordered Structures