The effect of non-linear capacitances in the localization properties of aperiodic dual electric transmission lines

Edmundo Lazo (), Alejandro Garrido and Félix Neira
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Edmundo Lazo: Departamento de Física, Facultad de Ciencias, Universidad de Tarapacá
Alejandro Garrido: Departamento de Física, Facultad de Ciencias, Universidad de Tarapacá
Félix Neira: Departamento de Física, Facultad de Ciencias, Universidad de Tarapacá

The European Physical Journal B: Condensed Matter and Complex Systems, 2016, vol. 89, issue 11, 1-6

Abstract: Abstract This study investigates the localization properties of dual electric transmission lines with non-linear capacitances. The V C,n voltage across each capacitor is selected as a non-linear function of the electric charge q n , i.e., V C,n = q n(1/C n -ε n |q n |2) where C n is the linear part of the capacitance and ε n the amplitude of the non-linear term. We follow a binary distribution of values of ε n , according to the Thue-Morse m-tupling sequence. The localization behavior of this non-linear case indicates that the case m = 2 does not belong to the m ≥ 3, family because when m changes from m = 2 to m = 3, the number of extended states diminishes dramatically. This proves the topological difference of the m = 2 and m = 3 families. However, by increasing m values, localization behavior of the m-tupling family resembles that of the m = 2, case because the system begins to regain its extended states. The exact same result was obtained recently in the study of linear direct transmission lines with m-tupling distribution of inductances. Consequently, we state that the localization behavior of the m-tupling family as a function of the m value is independent of both the linear and the non-linear system under study, but independent of the kind of transmission line (dual or direct). This is curious behavior of the m-tupling family and thus deserves more scholarly attention.

Keywords: Solid; State; and; Materials (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1140/epjb/e2016-70161-0

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