Eur. Phys. J. Plus (2019) 134: 28
https://doi.org/10.1140/epjp/i2019-12417-5

Regular Article

Disordered mixed transmission lines: localization behavior

Departamento de Física, Facultad de Ciencias, Universidad de Tarapacá, Arica, Chile

^* e-mail: edmundolazon@gmail.com

Received: 9 August 2018
Accepted: 20 November 2018
Published online: 17 January 2019

Abstract

We introduce a new type of transmission line: the mixed transmission line. This system is formed by the repetition of a set of p successive direct cells followed by q successive dual cells. The total number of cells N of the complete system arises from , where is the number of recurrence pattern and number of cells forming the basic unit of the mixed transmission lines. Our model allows introducing the disorder in any component of the dual or direct cells of the mixed transmission line. We study the localization behavior of this new model by introducing two different non-periodic distributions on the values of inductances of dual cells, namely the Aubry-André and the Fibonacci models. For random and non-periodic distributions of values, states were allowed to appear only inside a set of sub-bands separated by gaps in the frequency range. We study the localization behavior for the and cases. For (greater number of direct cells than dual cells), the d sub-bands are distributed more evenly in a reduced range of frequencies compared to . Using the scaling analysis of the average overlap amplitude, we have shown that for random distribution of q values of inductances of the dual cells, the extended states can appear in any of the d sub-band bands, but only for the small N -size system. We have further shown that the case , q = 1 for random distribution of q inductances , cannot be regarded as a model of Anderson diluted, because the localization behavior of both models is completely different.