Structure and diffusion time scales of disordered clusters

The eigenvalue spectra of the transition probability matrix for random walks traversing critically disordered clusters in three different types of percolation problems show that the random walker sees a developing Euclidean signature for short time scales as the local, full-coordination constraint is iteratively applied.Comment: 5 pages, 4 figures, submitted to Physics Letters

Quantum interference effects in particle transport through square lattices

We study the transport of a quantum particle through square lattices of various sizes by employing the tight-binding Hamiltonian from quantum percolation. Input and output semi-infinite chains are attached to the lattice either by diagonal point to point contacts or by a busbar connection. We find resonant transmission and reflection occuring whenever the incident particle's energy is near an eigenvalue of the lattice alone (i.e., the lattice without the chains attached). We also find the transmission to be strongly dependent on the way the chains are attached to the lattice.Comment: 4 pages, 6 figures, submitted to Phys. Rev.

Geometry of fully coordinated, two-dimensional percolation

We study the geometry of the critical clusters in fully coordinated percolation on the square lattice. By Monte Carlo simulations (static exponents) and normal mode analysis (dynamic exponents), we find that this problem is in the same universality class with ordinary percolation statically but not so dynamically. We show that there are large differences in the number and distribution of the interior sites between the two problems which may account for the different dynamic nature.Comment: ReVTeX, 5 pages, 6 figure

Quantum transport in randomly diluted quantum percolation clusters in two dimensions

We study the hopping transport of a quantum particle through finite, randomly diluted percolation clusters in two dimensions. We investigate how the transmission coefficient T behaves as a function of the energy E of the particle, the occupation concentration p of the disordered cluster, the size of the underlying lattice, and the type of connection chosen between the cluster and the input and output leads. We investigate both the point-to-point contacts and the busbar type of connection. For highly diluted clusters we find the behavior of the transmission to be independent of the type of connection. As the amount of dilution is decreased we find sharp variations in transmission. These variations are the remnants of the resonances at the ordered, zero-dilution, limit. For particles with energies within 0.25 \u3c= E \u3c= 1.75 (relative to the hopping integral) and with underlying square lattices of size 20 x 20, the configurations begin transmitting near p(alpha) = 0.60 with T against p curves following a common pattern as the amount of dilution is decreased. Near p(beta) = 0.90 this pattern is broken and the transmission begins to vary with the energy. In the asymptotic limit of very large clusters we find the systems to be totally reflecting in almost all cases. A few clear exceptions we find are when the amount of dilution is very low, when the particle has energy close to a resonance value at the ordered limit, and when the particle has energy at the middle of the band. These three cases, however, may not exhaust all possible exceptions. (c) 2007 Elsevier B.V. All rights reserved

Quantum transport in honeycomb lattice ribbons with armchair and zigzag edges coupled to semi-infinite linear chain leads

73.23.-b Electronic transport in mesoscopic systems, 73.63.-b Electronic transport in nanoscale materials and structures, 05.60.Gg Quantum transport,