**Edmundo Lazo**

Departamento de Física, Facultad de Ciencias, Universidad de Tarapacá, Arica, Box 6-D, Chile; edmundolazon@gmail.com or elazo@academicos.uta.cl

Received: 7 September 2019; Accepted: 1 October 2019; Published: 9 October 2019

**Abstract:** The properties of localization of the *<sup>I</sup>*(*ω*) electric current function in non-periodic electrical transmission lines have been intensively studied in the last decade. The electric components have been distributed in several forms: (a) aperiodic, including self-similar sequences (Fibonacci and *m*-tuplingtupling Thue–Morse), (b) incommensurate sequences (Aubry–André and Soukoulis–Economou), and (c) long-range correlated sequences (binary discrete and continuous). The localization properties of the transmission lines were measured using typical diagnostic tools of quantum mechanics like normalized localization length, transmission coefficient, average overlap amplitude, etc. As a result, it has been shown that the localization properties of the classic electric transmission lines are similar to the one-dimensional tight-binding quantum model, but also features some differences. Hence, it is worthwhile to continue investigating disordered transmission lines. To explore new localization behaviors, we are now studying two different problems, namely the model of interacting hanging cells (consisting of a finite number of dual or direct cells hanging in random positions in the transmission line), and the parity-time symmetry problem (PT -symmetry), where resistances *Rn* are distributed according to gain-loss sequence ( *R*2*n* = + *R*, *R*2*n*−<sup>1</sup> = − *R*). This review presents some of the most important results on the localization behavior of the *<sup>I</sup>*(*ω*) electric current function, in dual, direct, and mixed classic transmission lines, when the electrical components are distributed non-periodically.

**Keywords:** non-periodic systems; localization properties; electrical transmission lines
