Generation of extended states in diluted transmission lines with distribution of inductances according to Galois sequences: Hamiltonian map approach

We study the localization properties of diluted direct transmission lines, when we distribute two values of inductances LA and LB, according to the aperiodic Galois sequence. When we dilute the aperiodic Galois system with (d−1) inductances with constant L0 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 L0≈(LA,LB), we find a set of extended states for finite Nd system size, which disappears when Nd→∞. For the case L0âªÂ¢(LA,LB), using the scaling behavior of the averaged participation number 〈D(ω)〉 and the scaling behavior of the averaged normalized participation number 〈ξ(ω)〉, we demonstrate the existence of extended states in the thermodynamic limit.