Localization in one-dimensional relativistic quantum mechanics

We present the relativistic analogue of Anderson localization in one dimension. We use Dirac equation to calculate the transmission probability for a spin-½ particle incident upon a rectangular barrier. Using the transfer matrix formalism, we numerically compute the transmission probability for the...

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Veröffentlicht in:The European physical journal. B, Condensed matter physics Condensed matter physics, 2020-02, Vol.93 (2), Article 20
Hauptverfasser: Mehta, Abhay, Joshi, Sandeep, Jain, Sudhir R.
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Sprache:eng
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Zusammenfassung:We present the relativistic analogue of Anderson localization in one dimension. We use Dirac equation to calculate the transmission probability for a spin-½ particle incident upon a rectangular barrier. Using the transfer matrix formalism, we numerically compute the transmission probability for the case of a large number of identical barriers spread randomly in one dimension. The particular case when the incident particle has three component momentum and shows spin-flip phenomena is also considered. Our calculations suggest that the incident relativistic particle shows localization behaviour similar to that of Anderson localization. A number of results which are generalizations of the non-relativistic case are also obtained. Graphical abstract
ISSN:1434-6028
1434-6036
DOI:10.1140/epjb/e2019-100564-4