Abstract

We study the localization properties of diluted direct transmission lines, when we distribute two values of inductances L-A and L-B, according to the aperiodic Galois sequence. When we dilute the aperiodic Galois system with (d - 1) inductances with constant L-0 value, we find d sub-bands and (d - 1) gaps; here d is the period of the distribution of the Galois sequence in the diluted system. Under the condition L-0 approximate to (L-A, L-B), we find a set of extended states for finite N-d system size, which disappears when N-d ->infinity. For the case L-0 >> (L-A, L-B), using the scaling behavior of the averaged participation number < D(omega)> and the scaling behavior of the averaged normalized participation number , we demonstrate the existence of extended states in the thermodynamic limit. (C) 2014 Elsevier B.V. All rights reserved.