Overlap amplitude and localization properties in aperiodic diluted and non-diluted direct electric transmission lines

In this work we study the relationship existing between the localization properties of the diluted and non-diluted direct electrical transmission lines with the overlap amplitude C_ij^ω=2|I_i^ωI_j^ω|, where I_j^ω is the amplitude of the electric current function at jth cell of the transmission line for the state with frequency ω. We distribute two values of inductances L_A and L_B, according to the generalized aperiodic Thue–Morse m-tupling sequence. We find that the behavior of C_i,j^ω is directly related to the localization properties of the aperiodic sequences measured by the ξ normalized participation number, the R_q Rényi entropies and the μ_q moments. In addition, we generalize the scaling relationship for the overlap amplitude C_i,j^ω, i.e., 〈(C_i,j^ω)^2q〉=(2N)^2q.