  We study quantum percolation which is described by a tight-binding
Hamiltonian containing only off-diagonal hopping terms that are generally in
quenched binary disorder (zero or one). In such a system, transmission of a
quantum 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, we
develop a visualization method whereby the progression of a wave packet
entering the cluster through a lead on one side and exiting from another lead
on the other side can be tracked dynamically. Using this method, we investigate
the evolution of the wave packet through transmission and reflection under
clusters of various disorder, sizes, boundary conditions, and energies. Our
results indicate the existence of two different kinds of localized regimes,
namely exponential and power law localization, depending on the amount of
disorder. Our study further suggests that there may be a delocalized state in
the 2D quantum percolation system at very low disorder. These results are based
on a finite size scaling analysis of the systems of size up to 70 x 70
(containing 4900 sites) on the square lattice.
