Eur. Phys. J. D (2017) 71: 145
https://doi.org/10.1140/epjd/e2017-70820-8

Regular Article

Accurate measurement of the localization properties of electric transmission lines using the overlap amplitude

Departamento de Física, Facultad de Ciencias, Universidad de Tarapacá, Casilla 7 D Arica, Chile

^a e-mail: edmundolazon@gmail.com

Received: 28 December 2016
Published online: 9 June 2017

Abstract

We determine the localization properties of classic direct electric transmission lines by means of the overlap amplitude. The amplitude is defined as C_i,j^ω = 2|I_i^ωI_j^ω|, where I_i^ω is the electric current in the ith cell of the transmission line for the state with frequency ω. This definition is motivated by the concurrence C_i,j^α = 2|φ_i^αφ_j^α|, which is a quantum correlation measure (pairwise entanglement). We distribute the inductances L_j according to three non-linear models: (a) the slowly varying potential model; (b) the Aubry-André model and (c) the Soukoulis-Economou model. The results show that the average of the powers of the overlap amplitude ⟨(C_i,j^ω)^2q⟩ and its scaling properties may accurately characterize the localization behavior of these non-linear models. Moreover, the overlap amplitude can be used to determine the mobility edge of some non-periodic models.