Localization properties of transmission lines with generalized Thue-Morse distribution of inductances

We study the localization properties of direct transmission lines when we distribute twovalues of inductances L_A and L_B according to a generalized Thue-Morse aperiodic sequence generated by the inflation rule: A → AB^m−1, B → BA^m−1, m ≥ 2 and integer. We regain the usual Thue-Morse sequence for m = 2. We numerically study the changes produced in the localization properties of the I (ω) electric current function with increasing m values. We demonstrate that the m = 2 case does not belong to the family m ≥ 3, because when m changes from m = 2 to m = 3, the number of extended states decreasessignificantly. However, for m ≫ 3, the localization properties become similar to the m = 2 case. Also, the〈T〉 frequency averaged transmission coefficient shows a strong dependence from the N system size andfrom the m value which characterize each m-tupling sequence. In addition, for all m value studied, usingthe scaling behavior of the ξ (ω) normalized participation number, the R_q (ω) Rényi entropies and the μq (ω) moments, we have demonstrated the existence of extended states for certain specific frequencies.