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Disordered mixed transmission lines: localization behavior

  • E. LazoEmail author
  • F. Cortés-Cortés
Regular Article
  • 26 Downloads

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 \( N=dN_{s}\), where \( N_{s}\) is the number of recurrence pattern and \( d=(p+q)\) 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 \( L_{n,y}\) inductances of dual cells, namely the Aubry-André and the Fibonacci models. For random and non-periodic distributions of \( L_{n,y}\) values, states were allowed to appear only inside a set of \( d=(p+q)\) sub-bands separated by gaps in the frequency range. We study the localization behavior for the \( p > q\) and \( q > p\) cases. For \( p > q\) (greater number of direct cells than dual cells), the d sub-bands are distributed more evenly in a reduced range of frequencies compared to \( p < q\). Using the scaling analysis of the \( C_{\omega}\) average overlap amplitude, we have shown that for random distribution of q values of inductances \( L_{n,y}\) 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 \( p\geq 1\), q = 1 for random distribution of q inductances \( L_{n,y}\), cannot be regarded as a model of Anderson diluted, because the localization behavior of both models is completely different.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de Física, Facultad de CienciasUniversidad de TarapacáAricaChile

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