Eur. Phys. J. B (2015) 88: 216
https://doi.org/10.1140/epjb/e2015-60080-y

Regular Article

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

¹ Departamento de Física, Facultad de Ciencias, Universidad de Tarapacá, Arica, Chile
² Departamento de Física, Universidad de Santiago de Chile, Santiago, Chile
³ Escuela Universitaria de Ingeniería Mecánica, Universidad de Tarapacá, Arica, Chile

^a e-mail: elazo@uta.cl

Received: 30 January 2015
Received in final form: 10 June 2015
Published online: 2 September 2015

Abstract

We study the localization properties of direct transmission lines when we distribute two values of inductances L_A and L_B according to a generalized Thue-Morse aperiodic sequence generated by the inflation rule: A → ABm−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 decreases significantly. 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 and from the m value which characterize each m-tupling sequence. In addition, for all m value studied, using the scaling behavior of the ξ (ω) normalized participation number, the Rq (ω) Rényi entropies and the μq (ω) moments, we have demonstrated the existence of extended states for certain specific frequencies.