PERFECT CONDUCTANCE ON FRACTAL LATTICES

The Greenwood-Peierls conductance sum g is computed exactly on regular fractal lattices. While conductance g at any energy outside the infinite lattice spectrum scales with lattice size L in the superlocalized way, g similar to exp(-kappa L(alpha)), it is found that g similar to L beta for an infinite set of energies within the spectrum. Both the exponents beta and the corresponding energies for power-law scaling are found from an analysis of bounded orbits of a polynomial map. Interesting scaling behaviors include cross-over in which g similar to L(beta 1) for L out to L(c) and then g similar to L(beta 2). If beta(1) and beta(2) are two possible scaling behaviors, then arbitrarily close to each energy E(1) such that g similar to L(beta 1) there is E(2) such that g similar to L(beta 2) and an E(3) such that g similar to exp(-kappa L(alpha)). Thus there are no mobility edges. However there is an infinite set of energies at which beta = O so that g is independent of lattice size L.