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 L_A and L_B, 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≈(L_A,L_B), we find a set of extended states for finite N_d system size, which disappears when N_d→∞. For the case L₀⪢(L_A,L_B), 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