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

•We obtain the overlap amplitude 〈(Cijω)2q〉 as a function of the moments μqμq and the Rényi entropies RqRq.•We have found the scaling relationship for arbitrary order q  , namely 〈(Cijω)2q〉=(2N)2q.•The overlap amplitude 〈(Cijω)〉 and the normalized participation number ξ(ω)ξ(ω) are directly proportional magnitudes.•We have shown that the overlap amplitude 〈(Cijω)2q〉 is capable to discriminate between extended states and localized states.

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 Cijω=2|IiωIjω|, where Ijω 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 LALA and LBLB, according to the generalized aperiodic Thue–Morse m  -tupling sequence. We find that the behavior of Ci,jω is directly related to the localization properties of the aperiodic sequences measured by the ξ   normalized participation number, the RqRq Rényi entropies and the μqμq moments. In addition, we generalize the scaling relationship for the overlap amplitude Ci,jω, i.e., 〈(Ci,jω)2q〉=(2N)2q.