Response Function and Conductance of a Fibonacci Lattice

Abstract

A power law with respect to length n is numerically observed in the off-diagonal term of the one-particle Green’s function g_l,l±n(E) (E: energy, l: lattice site) and in the resistance r(n, E) and conductance g(n, E) of a Fibonacci lattice. The exponent is insensitive to energy, and the power law crosses over an exponential law at a length n^*(E)=1⁄A(E), where A(E) is a Lyapunov exponent which is strongly energy-sensitive. As a result, power law conductivity and resistivity with respect to temperature T are expected to be observed over a suitable range of temperatures.