Relationship between electron flux and electron complexity in a disordered Dirac comb

A. A. Heredia, C. V. Landauro, H. Nowak

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The transfer matrix method is used to calculate the electronic states of a finite chain of structurally disordered delta-function potentials. With the probability density for the electrons in the chain we calculate a complexity measure C for a continuous probability distribution, defined by a function of Shannon's entropy H, as an order measure of the chain, and the inverse participation ratio, or disequilibrium D, as a measure of localization of electron states. C is minimal for a completely ordered and maximal for a completely disordered chain. It is used as an indicator for the electronic transport in disordered systems characterized by a disorder parameter W. We also compare C with the transmission coefficient, T, and the inverse participation ratio D. A statistical interpretation is formulated based on the relationship between the disorder in the delta-function potentials and the transmitted and reflected electron flux. Hence, we are able to interpret the behavior of C with the formation of localized Gaussian distribution of the transmitted and reflected electron current j for growing disorder W.

Original languageEnglish
Article number125499
JournalPhysica A: Statistical Mechanics and its Applications
StatePublished - 15 Feb 2021
Externally publishedYes

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© 2020 Elsevier B.V.


  • Electron flux
  • Statistical complexity
  • Structural disorder


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