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We study quantum percolation which is described by a tight-bindingHamiltonian containing only off-diagonal hopping terms that are generally inquenched binary disorder (zero or one). In such a system, transmission of aquantum particle is determined by the disorder and interference effects,leading to interesting sharp features in conductance as the energy, disorder,and boundary conditions are varied. To aid understanding of this phenomenon, wedevelop a visualization method whereby the progression of a wave packetentering the cluster through a lead on one side and exiting from another leadon the other side can be tracked dynamically. Using this method, we investigatethe evolution of the wave packet through transmission and reflection underclusters of various disorder, sizes, boundary conditions, and energies. Ourresults indicate the existence of two different kinds of localized regimes,namely exponential and power law localization, depending on the amount ofdisorder. Our study further suggests that there may be a delocalized state inthe 2D quantum percolation system at very low disorder. These results are basedon a finite size scaling analysis of the systems of size up to 70 x 70(containing 4900 sites) on the square lattice.

Propagation of a quantum particle through two dimensional percolating systems